### B.2 Demonstration Functions

demo name
demo name n
demo ("name")
demo ("name", n)

  Run example code block n associated with the function name.

  If n is not specified, all examples are run.

  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’s load path. To separate examples from regular script code all lines are prefixed by `%!`. 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:

      %!demo
      %! t = 0:0.01:2*pi;
      %! x = sin (t);
      %! plot (t, x);
      %! title ("one cycle of a sine wave");
      %! #-------------------------------------------------
      %! # the figure window shows one cycle of a sine wave

  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 `title` or `text`. It is generally not necessary to use `disp` or `printf` within the demo.

  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

      %! input ("Press <enter> to continue: ", "s");

  between the sections, but this usage is discouraged. Other techniques to avoid multiple initialization blocks include using multiple plots with a new `figure` command between each plot, or using `subplot` to put multiple plots in the same window.

  Finally, because `demo` 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 must be used then the code `eval (example ("function", n))` will allow Octave to see them. This has its own problems, however, as `eval` only evaluates one line or statement at a time. In this case the function declaration must be wrapped with `"if 1 <demo stuff> endif"` where `"if"` is on the same line as `"demo"`. For example:

      %!demo if 1
      %!  function y = f(x)
      %!    y = x;
      %!  endfunction
      %!  f(3)
      %! endif

  See also: rundemos, example, test.

example name
example name n
example ("name")
example ("name", n)
[s, idx] = example (…)

  Display the code for example n associated with the function name, but do not run it.

  If n is not specified, all examples are displayed.

  When called with output arguments, the examples are returned in the form of a string s, with idx indicating the ending position of the various examples.

  See `demo` for a complete explanation.

  See also: demo, test.

rundemos ()
rundemos (directory)

  Execute built-in demos for all m-files in the specified directory.

  Demo blocks in any C++ source files (`*.cc`) will also be executed for use with dynamically linked oct-file functions.

  If no directory is specified, operate on all directories in Octave’s search path for functions.

  See also: demo, runtests, path.

runtests ()
runtests (directory)

  Execute built-in tests for all m-files in the specified directory.

  Test blocks in any C++ source files (`*.cc`) will also be executed for use with dynamically linked oct-file functions.

  If no directory is specified, operate on all directories in Octave’s search path for functions.

  See also: rundemos, test, path.

speed (f, init, max_n, f2, tol)
[order, n, T_f, T_f2] = speed (…)

  Determine the execution time of an expression (f) for various input values (n).

  The n are log-spaced from 1 to max_n. For each n, an initialization expression (init) is computed to create any data needed for the test. If a second expression (f2) 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.

  `f`

    The code expression to evaluate.

  `max_n`

    The maximum test length to run. The default value is 100. Alternatively, use `[min_n, max_n]` or specify the n exactly with `[n1, n2, …, nk]`.

  `init`

    Initialization expression for function argument values. Use k for the test number and n for the size of the test. This should compute values for all variables used by f. Note that init will be evaluated first for k = 0, so things which are constant throughout the test series can be computed once. The default value is `x = randn (n, 1)`.

  `f2`

    An alternative expression to evaluate, so that the speed of two expressions can be directly compared. The default is `[]`.

  `tol`

    Tolerance used to compare the results of expression f and expression f2. If tol is positive, the tolerance is an absolute one. If tol is negative, the tolerance is a relative one. The default is `eps`. If tol is `Inf`, then no comparison will be made.

  `order`

    The time complexity of the expression O(a*n^p). This is a structure with fields `a` and `p`.

  `n`

    The values n for which the expression was calculated AND the execution time was greater than zero.

  `T_f`

    The nonzero execution times recorded for the expression f in seconds.

  `T_f2`

    The nonzero execution times recorded for the expression f2 in seconds. If required, the mean time ratio is simply `mean (T_f ./ T_f2)`.

  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).

      speed ("for i = 1:n, y{i} = x(i); endfor", "", [1000, 10000])

  But it is if you preallocate the cell array `y`:

      speed ("for i = 1:n, y{i} = x(i); endfor", ...
             "x = rand (n, 1); y = cell (size (x));", [1000, 10000])

  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 `n`. For example:

      speed ("airy(x)", "x = rand (n, 10)", [10000, 100000])

  When comparing two different expressions (f, f2), 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:

      speed ("sum (x)", "", [10000, 100000], ...
             "v = 0; for i = 1:length (x), v += x(i); endfor")

  The following is a more complex example. If there was an original version of `xcorr` 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:

      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)

  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 `100*eps`. In this case, the comparison should be computed relatively, as `abs ((x - y) ./ y)` rather than absolutely as `abs (x - y)`.

  Type `example ("speed")` to see some real examples or `demo ("speed")` to run them.