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<p>
Previous: <a rel="previous" accesskey="p" href="Test-Functions.html#Test-Functions">Test Functions</a>,
Up: <a rel="up" accesskey="u" href="Test-and-Demo-Functions.html#Test-and-Demo-Functions">Test and Demo Functions</a>
<hr>
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<h3 class="section">B.2 Demonstration Functions</h3>
<!-- demo scripts/testfun/demo.m -->
<p><a name="doc_002ddemo"></a>
<div class="defun">
— Command: <b>demo</b><var> name<a name="index-demo-3390"></a></var><br>
— Command: <b>demo</b><var> name n<a name="index-demo-3391"></a></var><br>
— Function File: <b>demo</b> (<var>'name'</var>)<var><a name="index-demo-3392"></a></var><br>
— Function File: <b>demo</b> (<var>'name', n</var>)<var><a name="index-demo-3393"></a></var><br>
<blockquote>
<p>Run example code block <var>n</var> associated with the function <var>name</var>.
If <var>n</var> is not specified, all examples are run.
<p>Examples are stored in the script file, or in a file with the same
name but no extension located on Octave's load path. To keep examples
separate from regular script code, all lines are prefixed by <code>%!</code>. Each
example must also be introduced by the keyword 'demo' flush left to the
prefix with no intervening spaces. The remainder of the example can
contain arbitrary Octave code. For example:
<pre class="example"> %!demo
%! t=0:0.01:2*pi; x = sin (t);
%! plot (t,x)
%! %-------------------------------------------------
%! % the figure window shows one cycle of a sine wave
</pre>
<p>Note that the code is displayed before it is executed, so a simple
comment at the end suffices for labeling what is being shown. It is
generally not necessary to use <code>disp</code> or <code>printf</code> within the demo.
<p>Demos are run in a 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
<pre class="example"> %! input("Press <enter> to continue: ","s");
</pre>
<p class="noindent">between the sections, but this 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>Also, because demo evaluates within a function context, you cannot
define new functions inside a demo. If you must have function blocks,
rather than just anonymous functions or inline functions, you will have to
use <code>eval(example('function',n))</code> to see them. Because eval only
evaluates one line, or one statement if the statement crosses
multiple lines, you must wrap your demo in "if 1 <demo stuff> endif"
with the 'if' on the same line as 'demo'. For example:
<pre class="example"> %!demo if 1
%! function y=f(x)
%! y=x;
%! endfunction
%! f(3)
%! endif
</pre>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dtest.html#doc_002dtest">test</a>, <a href="doc_002dexample.html#doc_002dexample">example</a>.
</p></blockquote></div>
<!-- example scripts/testfun/example.m -->
<p><a name="doc_002dexample"></a>
<div class="defun">
— Command: <b>example</b><var> name<a name="index-example-3394"></a></var><br>
— Command: <b>example</b><var> name n<a name="index-example-3395"></a></var><br>
— Function File: <b>example</b> (<var>'name'</var>)<var><a name="index-example-3396"></a></var><br>
— Function File: <b>example</b> (<var>'name', n</var>)<var><a name="index-example-3397"></a></var><br>
— Function File: [<var>s</var>, <var>idx</var>] = <b>example</b> (<var><small class="dots">...</small></var>)<var><a name="index-example-3398"></a></var><br>
<blockquote>
<p>Display the code for example <var>n</var> associated with the function
'<var>name</var>', but do not run it. If <var>n</var> is not specified, all examples
are displayed.
<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>See <code>demo</code> for a complete explanation.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002ddemo.html#doc_002ddemo">demo</a>, <a href="doc_002dtest.html#doc_002dtest">test</a>.
</p></blockquote></div>
<!-- rundemos scripts/testfun/rundemos.m -->
<p><a name="doc_002drundemos"></a>
<div class="defun">
— Function File: <b>rundemos</b> ()<var><a name="index-rundemos-3399"></a></var><br>
— Function File: <b>rundemos</b> (<var>directory</var>)<var><a name="index-rundemos-3400"></a></var><br>
<blockquote><p>Execute built-in demos for all function files in the specified directory.
If no directory is specified, operate on all directories in Octave's
search path for functions.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002druntests.html#doc_002druntests">runtests</a>, <a href="doc_002dpath.html#doc_002dpath">path</a>.
</p></blockquote></div>
<!-- runtests scripts/testfun/runtests.m -->
<p><a name="doc_002druntests"></a>
<div class="defun">
— Function File: <b>runtests</b> ()<var><a name="index-runtests-3401"></a></var><br>
— Function File: <b>runtests</b> (<var>directory</var>)<var><a name="index-runtests-3402"></a></var><br>
<blockquote><p>Execute built-in tests for all function files in the specified directory.
If no directory is specified, operate on all directories in Octave's
search path for functions.
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002drundemos.html#doc_002drundemos">rundemos</a>, <a href="doc_002dpath.html#doc_002dpath">path</a>.
</p></blockquote></div>
<!-- speed scripts/testfun/speed.m -->
<p><a name="doc_002dspeed"></a>
<div class="defun">
— Function File: <b>speed</b> (<var>f, init, max_n, f2, tol</var>)<var><a name="index-speed-3403"></a></var><br>
— Function File: [<var>order</var>, <var>n</var>, <var>T_f</var>, <var>T_f2</var>] = <b>speed</b> (<var><small class="dots">...</small></var>)<var><a name="index-speed-3404"></a></var><br>
<blockquote>
<p>Determine the execution time of an expression (<var>f</var>) for various input
values (<var>n</var>). 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.
<dl>
<dt><var>f</var><dd>The code expression to evaluate.
<br><dt><var>max_n</var><dd>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, ..., nk]</code>.
<br><dt><var>init</var><dd>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 k = 0, so things which are constant throughout
the test series can be computed once. The default value is
<var>x</var><code> = randn (</code><var>n</var><code>, 1)</code>.
<br><dt><var>f2</var><dd>An alternative expression to evaluate, so that the speed of two
expressions can be directly compared. The default is <code>[]</code>.
<br><dt><var>tol</var><dd>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.
<br><dt><var>order</var><dd>The time complexity of the expression O(a*n^p). This
is a structure with fields <code>a</code> and <code>p</code>.
<br><dt><var>n</var><dd>The values <var>n</var> for which the expression was calculated <strong>AND</strong>
the execution time was greater than zero.
<br><dt><var>T_f</var><dd>The nonzero execution times recorded for the expression <var>f</var> in seconds.
<br><dt><var>T_f2</var><dd>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>.
</dl>
<p>The slope of the execution time graph shows the approximate
power of the asymptotic running time O(n^p). 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 O(n^2)
rather than O(n) 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 O(n).
<pre class="example"> speed ("for i = 1:n, y{i} = x(i); endfor", "", [1000, 10000])
</pre>
<p class="noindent">But it is if you preallocate the cell array <code>y</code>:
<pre class="example"> speed ("for i = 1:n, y{i} = x(i); endfor", ...
"x = rand (n, 1); y = cell (size (x));", [1000, 10000])
</pre>
<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:
<pre class="example"> speed ("airy(x)", "x = rand (n, 10)", [10000, 100000])
</pre>
<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:
<pre class="example"> speed ("sum (x)", "", [10000, 100000], ...
"v = 0; for i = 1:length (x), v += x(i); endfor")
</pre>
<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:
<pre class="example"> speed ("xcorr (x, n)", "x = rand (128, 1);", 100,
"xcorr_orig (x, n)", -100*eps)
speed ("xcorr (x, 15)", "x = rand (20+n, 1);", 100,
"xcorr_orig (x, n)", -100*eps)
</pre>
<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 ((</code><var>x</var><code> - </code><var>y</var><code>) ./ </code><var>y</var><code>)</code> rather
than absolutely as <code>abs (</code><var>x</var><code> - </code><var>y</var><code>)</code>.
<p>Type <kbd>example ("speed")</kbd> to see some real examples or
<kbd>demo ("speed")</kbd> to run them.
</p></blockquote></div>
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