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@c Copyright (C) 2002-2005 Paul Kienzle
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@node Test and Demo Functions
@appendix Test and Demo Functions
@cindex test functions

Octave includes a number of functions to allow the integration of testing
and demonstration code in the source code of the functions themselves.

@menu
* Test Functions::
* Demonstration Functions::
@end menu

@node Test Functions
@section Test Functions

@c test scripts/testfun/test.m
@anchor{XREFtest}
@deftypefn  {Command} {} test @var{name}
@deftypefnx {Command} {} test @var{name} quiet|normal|verbose
@deftypefnx {Function File} {} test ("@var{name}", "quiet|normal|verbose", @var{fid})
@deftypefnx {Function File} {} test ([], "explain", @var{fid})
@deftypefnx {Function File} {@var{success} =} test (@dots{})
@deftypefnx {Function File} {[@var{n}, @var{max}] =} test (@dots{})
@deftypefnx {Function File} {[@var{code}, @var{idx}] =} test ("@var{name}", "grabdemo")

Perform tests from the first file in the loadpath matching @var{name}.
@code{test} can be called as a command or as a function.  Called with
a single argument @var{name}, the tests are run interactively and stop
after the first error is encountered.

With a second argument the tests which are performed and the amount of
output is selected.

@table @asis
@item @qcode{"quiet"}
 Don't report all the tests as they happen, just the errors.

@item @qcode{"normal"}
Report all tests as they happen, but don't do tests which require
user interaction.

@item @qcode{"verbose"}
Do tests which require user interaction.
@end table

The argument @var{fid} can be used to allow batch processing.  Errors
can be written to the already open file defined by @var{fid}, and
hopefully when Octave crashes this file will tell you what was happening
when it did.  You can use @code{stdout} if you want to see the results as
they happen.  You can also give a file name rather than an @var{fid}, in
which case the contents of the file will be replaced with the log from
the current test.

Called with a single output argument @var{success}, @code{test} returns
true if all of the tests were successful.  Called with two output arguments
@var{n} and @var{max}, the number of successful tests and the total number
of tests in the file @var{name} are returned.

If the second argument is the string @qcode{"grabdemo"}, the contents of
the demo blocks are extracted but not executed.  Code for all code blocks
is concatenated and returned as @var{code} with @var{idx} being a vector
of positions of the ends of the demo blocks.

If the second argument is @qcode{"explain"}, then @var{name} is ignored
and an explanation of the line markers used is written to the file
@var{fid}.
@seealso{@ref{XREFassert,,assert}, @ref{XREFfail,,fail}, @ref{XREFerror,,error}, @ref{XREFdemo,,demo}, @ref{XREFexample,,example}}
@end deftypefn


@code{test} scans the named script file looking for lines which start
with the identifier @samp{%!}.  The prefix is stripped off and the rest
of the line is processed through the Octave interpreter.  If the code
generates an error, then the test is said to fail.

Since @code{eval()} will stop at the first error it encounters, you must
divide your tests up into blocks, with anything in a separate
block evaluated separately.  Blocks are introduced by valid keywords like
@code{test}, @code{function}, or @code{assert} immediately following @samp{%!}.
A block is defined by indentation as in Python.  Lines beginning with
@samp{%!<whitespace>} are part of the preceeding block.
 
For example:

@example
@group
%!test error ("this test fails!");
%!test "test doesn't fail. it doesn't generate an error";
@end group
@end example

When a test fails, you will see something like:

@example
@group
  ***** test error ("this test fails!")
!!!!! test failed
this test fails!
@end group
@end example

Generally, to test if something works, you want to assert that it
produces a correct value.  A real test might look something like

@example
@group
%!test
%! @var{a} = [1, 2, 3; 4, 5, 6]; B = [1; 2];
%! expect = [ @var{a} ; 2*@var{a} ];
%! get = kron (@var{b}, @var{a});
%! if (any (size (expect) != size (get)))
%!   error ("wrong size: expected %d,%d but got %d,%d",
%!          size (expect), size (get));
%! elseif (any (any (expect != get)))
%!   error ("didn't get what was expected.");
%! endif
@end group
@end example

To make the process easier, use the @code{assert} function.  For example,
with @code{assert} the previous test is reduced to:

@example
@group
%!test
%! @var{a} = [1, 2, 3; 4, 5, 6]; @var{b} = [1; 2];
%! assert (kron (@var{b}, @var{a}), [ @var{a}; 2*@var{a} ]);
@end group
@end example

@code{assert} can accept a tolerance so that you can compare results
absolutely or relatively.  For example, the following all succeed:

@example
@group
%!test assert (1+eps, 1, 2*eps)          # absolute error
%!test assert (100+100*eps, 100, -2*eps) # relative error
@end group
@end example

You can also do the comparison yourself, but still have assert
generate the error:

@example
@group
%!test assert (isempty ([]))
%!test assert ([1, 2; 3, 4] > 0)
@end group
@end example

Because @code{assert} is so frequently used alone in a test block, there
is a shorthand form:

@example
%!assert (@dots{})
@end example

@noindent
which is equivalent to:

@example
%!test assert (@dots{})
@end example

Occasionally a block of tests will depend on having optional
functionality in Octave.  Before testing such blocks the availability of
the required functionality must be checked.  A @code{%!testif HAVE_XXX}
block will only be run if Octave was compiled with functionality
@samp{HAVE_XXX}.  For example, the sparse single value decomposition,
@code{svds()}, depends on having the @sc{arpack} library.  All of the tests
for @code{svds} begin with

@example
%!testif HAVE_ARPACK
@end example

@noindent
Review @file{config.h} or @code{octave_config_info ("features")} to see some
of the possible values to check.

Sometimes during development there is a test that should work but is
known to fail.  You still want to leave the test in because when the
final code is ready the test should pass, but you may not be able to
fix it immediately.  To avoid unnecessary bug reports for these known
failures, mark the block with @code{xtest} rather than @code{test}:

@example
@group
%!xtest assert (1==0)
%!xtest fail ("success=1", "error")
@end group
@end example

@noindent
In this case, the test will run and any failure will be reported.
However, testing is not aborted and subsequent test blocks will be
processed normally.  Another use of @code{xtest} is for statistical
tests which should pass most of the time but are known to fail
occasionally.

Each block is evaluated in its own function environment, which means
that variables defined in one block are not automatically shared
with other blocks.  If you do want to share variables, then you
must declare them as @code{shared} before you use them.  For example, the
following declares the variable @var{a}, gives it an initial value (default
is empty), and then uses it in several subsequent tests.

@example
@group
%!shared @var{a}
%! @var{a} = [1, 2, 3; 4, 5, 6];
%!assert (kron ([1; 2], @var{a}), [ @var{a}; 2*@var{a} ]);
%!assert (kron ([1, 2], @var{a}), [ @var{a}, 2*@var{a} ]);
%!assert (kron ([1,2; 3,4], @var{a}), [ @var{a},2*@var{a}; 3*@var{a},4*@var{a} ]);
@end group
@end example

You can share several variables at the same time:

@example
%!shared @var{a}, @var{b}
@end example

You can also share test functions:

@example
@group
%!function @var{a} = fn (@var{b})
%!  @var{a} = 2*@var{b};
%!endfunction
%!assert (fn(2), 4);
@end group
@end example

Note that all previous variables and values are lost when a new 
shared block is declared.

Remember that @code{%!function} begins a new block and that 
@code{%!endfunction} ends this block.  Be aware that until a new block
is started, lines starting with @samp{%!<space>} will be discarded as comments.
The following is nearly identical to the example above, but does nothing.

@example
@group
%!function @var{a} = fn (@var{b})
%!  @var{a} = 2*@var{b};
%!endfunction
%! assert (fn(2), 4);
@end group
@end example

@noindent
Because there is a space after @samp{%!} the @code{assert} statement does
not begin a new block and this line is treated as a comment.

Error and warning blocks are like test blocks, but they only succeed 
if the code generates an error.  You can check the text of the error
is correct using an optional regular expression @code{<pattern>}.  
For example:

@example
%!error <passes!> error ("this test passes!");
@end example

If the code doesn't generate an error, the test fails.  For example:

@example
%!error "this is an error because it succeeds.";
@end example

@noindent
produces

@example
@group
  ***** error "this is an error because it succeeds.";
!!!!! test failed: no error
@end group
@end example

It is important to automate the tests as much as possible, however
some tests require user interaction.  These can be isolated into
demo blocks, which if you are in batch mode, are only run when 
called with @code{demo} or the @code{verbose} option to @code{test}.
The code is displayed before it is executed.  For example,

@example
@group
%!demo
%! @var{t} = [0:0.01:2*pi]; @var{x} = sin (@var{t});
%! plot (@var{t}, @var{x});
%! # you should now see a sine wave in your figure window
@end group
@end example

@noindent
produces

@example
@group
funcname example 1:
 @var{t} = [0:0.01:2*pi]; @var{x} = sin (@var{t});
 plot (@var{t}, @var{x});
 # you should now see a sine wave in your figure window

Press <enter> to continue: 
@end group
@end example

Note that demo blocks cannot use any shared variables.  This is so
that they can be executed by themselves, ignoring all other tests.

If you want to temporarily disable a test block, put @code{#} in place
of the block type.  This creates a comment block which is echoed
in the log file but not executed.  For example:

@example
@group
%!#demo
%! @var{t} = [0:0.01:2*pi]; @var{x} = sin (@var{t});
%! plot (@var{t}, @var{x});
%! # you should now see a sine wave in your figure window
@end group
@end example

@noindent
The following trivial code snippet provides examples for the use of
fail, assert, error and xtest:

@example
@group
function output = must_be_zero (@var{input})
  if (@var{input} != 0)
    error ("Non-zero input!")
  endif
  output = input;
endfunction

%!fail ("must_be_zero (1)");
%!assert (must_be_zero (0), 0);
%!error <Non-zero> must_be_zero (1);
%!xtest error ("This code generates an error");
@end group
@end example

@noindent
When putting this a file @file{must_be_zero.m}, and running the test, we see

@example
@group
test must_be_zero verbose

@result{}
>>>>> /path/to/must_be_zero.m
  ***** fail ("must_be_zero (1)");
  ***** assert (must_be_zero (0), 0);
  ***** error <Non-zero> must_be_zero (1);
  ***** xtest error ("This code generates an error");
!!!!! known failure
This code generates an error
PASSES 4 out of 4 tests (1 expected failures)
@end group
@end example

@subsubheading Block type summary:

@table @code
@item %!test
check that entire block is correct

@item %!testif HAVE_XXX
check block only if Octave was compiled with feature HAVE_XXX.

@item %!xtest
check block, report a test failure but do not abort testing.

@item %!error
check for correct error message

@item %!warning
check for correct warning message

@item %!demo
demo only executes in interactive mode

@item %!#
comment: ignore everything within the block

@item %!shared x,y,z
declare variables for use in multiple tests

@item %!function
define a function for use in multiple tests

@item %!endfunction
close a function definition

@item %!assert (x, y, tol)
shorthand for @code{%!test assert (x, y, tol)}
@end table

You can also create test scripts for built-in functions and your own C++
functions.  To do so, put a file with the bare function name (no .m
extension) in a directory in the load path and it will be discovered by
the @code{test} function.  Alternatively, you can embed tests directly in your
C++ code:

@example
@group
/*
%!test disp ("this is a test")
*/
@end group
@end example

@noindent
or

@example
@group
#if 0
%!test disp ("this is a test")
#endif
@end group
@end example

@noindent
However, in this case the raw source code will need to be on the load
path and the user will have to remember to type
@code{test ("funcname.cc")}.

@c assert scripts/testfun/assert.m
@anchor{XREFassert}
@deftypefn  {Function File} {} assert (@var{cond})
@deftypefnx {Function File} {} assert (@var{cond}, @var{errmsg}, @dots{})
@deftypefnx {Function File} {} assert (@var{cond}, @var{msg_id}, @var{errmsg}, @dots{})
@deftypefnx {Function File} {} assert (@var{observed}, @var{expected})
@deftypefnx {Function File} {} assert (@var{observed}, @var{expected}, @var{tol})

Produce an error if the specified condition is not met.  @code{assert} can
be called in three different ways.

@table @code
@item  assert (@var{cond})
@itemx assert (@var{cond}, @var{errmsg}, @dots{})
@itemx assert (@var{cond}, @var{msg_id}, @var{errmsg}, @dots{})
Called with a single argument @var{cond}, @code{assert} produces an
error if @var{cond} is zero.  When called with more than one argument the
additional arguments are passed to the @code{error} function.

@item assert (@var{observed}, @var{expected})
Produce an error if observed is not the same as expected.  Note that
@var{observed} and @var{expected} can be scalars, vectors, matrices,
strings, cell arrays, or structures.

@item assert (@var{observed}, @var{expected}, @var{tol})
Produce an error if observed is not the same as expected but equality
comparison for numeric data uses a tolerance @var{tol}.
If @var{tol} is positive then it is an absolute tolerance which will produce
an error if @code{abs (@var{observed} - @var{expected}) > abs (@var{tol})}.
If @var{tol} is negative then it is a relative tolerance which will produce
an error if @code{abs (@var{observed} - @var{expected}) >
abs (@var{tol} * @var{expected})}.  If @var{expected} is zero @var{tol} will
always be interpreted as an absolute tolerance.  If @var{tol} is not scalar
its dimensions must agree with those of @var{observed} and @var{expected}
and tests are performed on an element-wise basis.
@end table
@seealso{@ref{XREFtest,,test}, @ref{XREFfail,,fail}, @ref{XREFerror,,error}}
@end deftypefn


@c fail scripts/testfun/fail.m
@anchor{XREFfail}
@deftypefn  {Function File} {} fail (@var{code})
@deftypefnx {Function File} {} fail (@var{code}, @var{pattern})
@deftypefnx {Function File} {} fail (@var{code}, "warning", @var{pattern})

Return true if @var{code} fails with an error message matching
@var{pattern}, otherwise produce an error.  Note that @var{code}
is a string and if @var{code} runs successfully, the error produced is:

@example
          expected error <.> but got none
@end example


Code must be in the form of a string that may be passed by
@code{fail} to the Octave interpreter via the @code{evalin} function,
that is, a (quoted) string constant or a string variable.

If called with two arguments, the behavior is similar to
@code{fail (@var{code})}, except the return value will only be true if
code fails with an error message containing pattern (case sensitive).
If the code fails with a different error to that given in pattern,
the message produced is:

@example
@group
          expected <pattern>
          but got <text of actual error>
@end group
@end example

The angle brackets are not part of the output.

Called with three arguments, the behavior is similar to
@code{fail (@var{code}, @var{pattern})}, but produces an error if no
warning is given during code execution or if the code fails.
@seealso{@ref{XREFassert,,assert}}
@end deftypefn


@node Demonstration Functions
@section Demonstration Functions

@c demo scripts/testfun/demo.m
@anchor{XREFdemo}
@deftypefn  {Command} {} demo @var{name}
@deftypefnx {Command} {} demo @var{name} @var{n}
@deftypefnx {Function File} {} demo ("@var{name}")
@deftypefnx {Function File} {} demo ("@var{name}", @var{n})

Run example code block @var{n} associated with the function @var{name}.
If @var{n} is not specified, all examples are run.

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{%!}.  Each
example must also be introduced by the keyword @qcode{"demo"} flush left
to the prefix with no intervening spaces.  The remainder of the example
can contain arbitrary Octave code.  For example:

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

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} or @code{printf} within the demo.

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

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

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

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))} to see them.  Because eval only
evaluates one line, or one statement if the statement crosses
multiple lines, you must wrap your demo in @qcode{"if 1 <demo stuff> endif"}
with the @qcode{"if"} on the same line as @qcode{"demo"}.  For example:

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

@seealso{@ref{XREFtest,,test}, @ref{XREFexample,,example}}
@end deftypefn


@c example scripts/testfun/example.m
@anchor{XREFexample}
@deftypefn  {Command} {} example @var{name}
@deftypefnx {Command} {} example @var{name} @var{n}
@deftypefnx {Function File} {} example ("@var{name}")
@deftypefnx {Function File} {} example ("@var{name}", @var{n})
@deftypefnx {Function File} {[@var{s}, @var{idx}] =} example (@dots{})

Display the code for example @var{n} associated with the function
@var{name}, but do not run it.  If @var{n} is not specified, all examples
are displayed.

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

See @code{demo} for a complete explanation.
@seealso{@ref{XREFdemo,,demo}, @ref{XREFtest,,test}}
@end deftypefn


@c rundemos scripts/testfun/rundemos.m
@anchor{XREFrundemos}
@deftypefn  {Function File} {} rundemos ()
@deftypefnx {Function File} {} rundemos (@var{directory})
Execute built-in demos for all function files in the specified directory.
Also executes demos in any C++ source files found in the directory, for
use with dynamically linked functions.

If no directory is specified, operate on all directories in Octave's
search path for functions.
@seealso{@ref{XREFruntests,,runtests}, @ref{XREFpath,,path}}
@end deftypefn


@c runtests scripts/testfun/runtests.m
@anchor{XREFruntests}
@deftypefn  {Function File} {} runtests ()
@deftypefnx {Function File} {} runtests (@var{directory})
Execute built-in tests for all function files in the specified directory.
Also executes tests in any C++ source files found in the directory, for
use with dynamically linked functions.

If no directory is specified, operate on all directories in Octave's
search path for functions.
@seealso{@ref{XREFrundemos,,rundemos}, @ref{XREFpath,,path}}
@end deftypefn


@c speed scripts/testfun/speed.m
@anchor{XREFspeed}
@deftypefn  {Function File} {} speed (@var{f}, @var{init}, @var{max_n}, @var{f2}, @var{tol})
@deftypefnx {Function File} {[@var{order}, @var{n}, @var{T_f}, @var{T_f2}] =} speed (@dots{})

Determine the execution time of an expression (@var{f}) for various input
values (@var{n}).  The @var{n} are log-spaced from 1 to @var{max_n}.  For
each @var{n}, an initialization expression (@var{init}) is computed to
create any data needed for the test.  If a second expression (@var{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.

@table @code
@item @var{f}
The code expression to evaluate.

@item @var{max_n}
The maximum test length to run.  The default value is 100.  Alternatively,
use @code{[min_n, max_n]} or specify the @var{n} exactly with
@code{[n1, n2, @dots{}, nk]}.

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

@item @var{f2}
An alternative expression to evaluate, so that the speed of two
expressions can be directly compared.  The default is @code{[]}.

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

@item @var{order}
The time complexity of the expression @math{O(a*n^p)}.  This
is a structure with fields @code{a} and @code{p}.

@item @var{n}
The values @var{n} for which the expression was calculated @strong{AND}
the execution time was greater than zero.

@item @var{T_f}
The nonzero execution times recorded for the expression @var{f} in seconds.

@item @var{T_f2}
The nonzero execution times recorded for the expression @var{f2} in seconds.
If required, the mean time ratio is simply @code{mean (T_f ./ T_f2)}.

@end table

The slope of the execution time graph shows the approximate
power of the asymptotic running time @math{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 @math{O(n^2)}
rather than @math{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 @math{O(n)}.

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

@noindent
But it is if you preallocate the cell array @code{y}:

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

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}.  For
example:

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

When comparing two different expressions (@var{f}, @var{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:

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

The following is a more complex example.  If there was an original version
of @code{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:

@example
@group
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)
@end group
@end example

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}.  In this case, the comparison should be
computed relatively, as @code{abs ((@var{x} - @var{y}) ./ @var{y})} rather
than absolutely as @code{abs (@var{x} - @var{y})}.

Type @kbd{example ("speed")} to see some real examples or 
@kbd{demo ("speed")} to run them.
@end deftypefn