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@c Copyright (C) 2005, 2007 David Bateman
@c Copyright (C) 2002, 2003, 2004, 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

@anchor{doc-test}
@deftypefn {Function File} {} test @var{name}
@deftypefnx {Function File} {} 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 'quiet'
 Don't report all the tests as they happen, just the errors.

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

@item '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 '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 'explain', then @var{name} is ignored and an
explanation of the line markers used is written to the file @var{fid}.
@seealso{error, assert, fail, demo, example}
@end deftypefn


@code{test} scans the named script file looking for lines which
start with @code{%!}. 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 the keyword
@code{test} immediately following the @code{%!}.  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

which is equivalent to:

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

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

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), 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};
   %!assert (@var{a}(2),4);
@end group
@end example

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

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

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 @code{verbose}. 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

produces

@example
@group
   > @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 is 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

Block type summary:

@table @code
@item %!test
check that entire block is correct
@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
declares variables for use in multiple tests
@item %!function
defines a function value for a shared variable
@item %!assert (x, y, tol)
shorthand for %!test assert (x, y, tol)
@end table

You can also create test scripts for builtins and your own C++
functions. Just put a file of the function name on your path without
any extension and it will be picked up by the test procedure.  You
can even embed tests directly in your C++ code:

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

or

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

but then the code will have to be on the load path and the user 
will have to remember to type test('name.cc').  Conversely, you
can separate the tests from normal octave script files by putting
them in plain files with no extension rather than in script files.
@c DO I WANT TO INCLUDE THE EDITOR SPECIFIC STATEMENT BELOW???
@c Don't forget to tell emacs that the plain text file you are using
@c is actually octave code, using something like:
@c   -*-octave-*-

@anchor{doc-assert}
@deftypefn {Function File} {} assert (@var{cond})
@deftypefnx {Function File} {} assert (@var{observed},@var{expected})
@deftypefnx {Function File} {} assert (@var{observed},@var{expected},@var{tol})

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

@table @code
@item assert (@var{cond})
Called with a single argument @var{cond}, @code{assert} produces an
error if @var{cond} is zero.

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

@item assert(@var{observed}, @var{expected}, @var{tol})
Accept a tolerance when comparing numbers. 
If @var{tol} is possitive use it as an absolute tolerance, will produce an error if
@code{abs(@var{observed} - @var{expected}) > abs(@var{tol})}.
If @var{tol} is negative use it as a relative tolerance, 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 used as an absolute tolerance.
@end table
@seealso{test}
@end deftypefn


@anchor{doc-fail}
@deftypefn {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

If the code fails with a different error, the message produced is:

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

@end deftypefn


@node Demonstration Functions
@section Demonstration Functions

@anchor{doc-demo}
@deftypefn {Function File} {} demo ('@var{name}',@var{n})

Runs any examples associated with the function '@var{name}'.  
Examples are stored in the script file, or in a file with the same 
name but no extension somewhere on your path.  To keep them separate 
from the usual script code, all lines are prefixed by @code{%!}. Each
example is 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:

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

Note that the code is displayed before it is executed, so a simple
comment at the end suffices.  It is generally not necessary to use
disp or printf within the demo.

Demos are run in a function environment with no access to external
variables. This means that all demos in your function must use
separate initialization code. Alternatively, you can combine your
demos into one huge demo, with the code:

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

between the sections, but this is discouraged.  Other techniques
include using multiple plots by saying figure between each, or
using subplot to put multiple plots in the same window.

Also, since demo evaluates inside a function context, you cannot
define new functions inside a demo.  Instead 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 "if 1 <demo stuff> endif"
with the 'if' on the same line as 'demo'. For example,

@example
  %!demo if 1
  %!  function y=f(x)
  %!    y=x;
  %!  endfunction
  %!  f(3)
  %! endif
@end example
@seealso{test, example}
@end deftypefn


@anchor{doc-example}
@deftypefn {Function File} {} example ('@var{name}',@var{n})
@deftypefnx {Function File} {[@var{x}, @var{idx}] =} example ('@var{name}',@var{n})

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

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

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


@anchor{doc-speed}
@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 for various @var{n}.
The @var{n} are log-spaced from 1 to @var{max_n}.  For each @var{n},
an initialization expression is computed to create whatever data
are needed for the test.  If a second expression is given, the
execution times of the two expressions will be compared.  Called 
without output arguments the results are presented graphically.

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

@item @var{max_n}
The maximum test length to run. Default value is 100.  Alternatively,
use @code{[min_n,max_n]} or for complete control, @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 listed in args.  Note that init will
be evaluated first for k=0, so things which are constant throughout
the test can be computed then. The default value is @code{@var{x} =
randn (@var{n}, 1);}.

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

@item @var{tol}
If @var{tol} is @code{Inf}, then no comparison will be made between the
results of expression @var{f} and expression @var{f2}.  Otherwise,
expression @var{f} should produce a value @var{v} and expression @var{f2} 
should produce a value @var{v2}, and these shall be compared using 
@code{assert(@var{v},@var{v2},@var{tol})}. If @var{tol} is positive,
the tolerance is assumed to be absolute. If @var{tol} is negative,
the tolerance is assumed to be relative. The default is @code{eps}.

@item @var{order}
The time complexity of the expression @code{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 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 it is needed, the mean time ratio is just @code{mean(T_f./T_f2)}.

@end table

The slope of the execution time graph shows the approximate
power of the asymptotic running time @code{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 your algorithm.  It should indicate if for 
example your implementation is unexpectedly @code{O(n^2)} 
rather than @code{O(n)} because it extends a vector each 
time through the loop rather than preallocating one which is 
big enough.  For example, in the current version of Octave,
the following is not the expected @code{O(n)}:

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

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

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

An attempt is made to approximate the cost of the 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 a new and original expression, 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 it will shift it relative to the original.  For
example:

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

A more complex example, if you had an original version of @code{xcorr}
using for loops and another version using an FFT, you could compare the
run speed for various lags as follows, or for a fixed lag with varying
vector lengths as follows:

@example
  speed("v=xcorr(x,n)", "x=rand(128,1);", 100, ...
        "v2=xcorr_orig(x,n)", -100*eps)
  speed("v=xcorr(x,15)", "x=rand(20+n,1);", 100, ...
        "v2=xcorr_orig(x,n)", -100*eps)
@end example

Assuming one of the two versions is in @var{xcorr_orig}, this
would compare their speed and their output values.  Note that the
FFT version is not exact, so we specify an acceptable tolerance on
the comparison @code{100*eps}, and the errors should be computed
relatively, as @code{abs((@var{x} - @var{y})./@var{y})} rather than 
absolutely as @code{abs(@var{x} - @var{y})}.

Type @code{example('speed')} to see some real examples. Note for 
obscure reasons, you can't run examples 1 and 2 directly using 
@code{demo('speed')}. Instead use, @code{eval(example('speed',1))}
and @code{eval(example('speed',2))}.
@end deftypefn



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