140 lines
5.0 KiB
Plaintext
140 lines
5.0 KiB
Plaintext
[section:error_test Relative Error and Testing]
|
|
|
|
[h4 Synopsis]
|
|
|
|
``
|
|
#include <boost/math/tools/test.hpp>
|
|
``
|
|
|
|
[important
|
|
The header `boost/math/tools/test.hpp` is located under `libs/math/include_private`
|
|
and is NOT installed to the usual locations by default; you will need to add `libs/math/include_private`
|
|
to your compiler's include path in order to use this header.]
|
|
|
|
template <class T>
|
|
T relative_error(T a, T b);
|
|
|
|
template <class A, class F1, class F2>
|
|
test_result<see-below> test(const A& a, F1 test_func, F2 expect_func);
|
|
|
|
[h4 Description]
|
|
|
|
template <class T>
|
|
T relative_error(T a, T v);
|
|
|
|
Returns the relative error between /a/ and /v/ using the usual formula:
|
|
|
|
[equation error1]
|
|
|
|
In addition the value returned is zero if:
|
|
|
|
* Both /a/ and /v/ are infinite.
|
|
* Both /a/ and /v/ are denormalised numbers or zero.
|
|
|
|
Otherwise if only one of /a/ and /v/ is zero then the value returned is 1.
|
|
|
|
template <class A, class F1, class F2>
|
|
test_result<see-below> test(const A& a, F1 test_func, F2 expect_func);
|
|
|
|
This function is used for testing a function against tabulated test data.
|
|
|
|
The return type contains statistical data on the relative errors (max, mean,
|
|
variance, and the number of test cases etc), as well as the row of test data that
|
|
caused the largest relative error. Public members of type test_result are:
|
|
|
|
[variablelist
|
|
[[`unsigned worst()const;`][Returns the row at which the worst error occurred.]]
|
|
[[`T min()const;`][Returns the smallest relative error found.]]
|
|
[[`T max()const;`][Returns the largest relative error found.]]
|
|
[[`T mean()const;`][Returns the mean error found.]]
|
|
[[`boost::uintmax_t count()const;`][Returns the number of test cases.]]
|
|
[[`T variance()const;`][Returns the variance of the errors found.]]
|
|
[[`T variance1()const;`][Returns the unbiased variance of the errors found.]]
|
|
[[`T rms()const`][Returns the Root Mean Square, or quadratic mean of the errors.]]
|
|
[[`test_result& operator+=(const test_result& t)`][Combines two test_result's into
|
|
a single result.]]
|
|
]
|
|
|
|
The template parameter of test_result, is the same type as the values in the two
|
|
dimensional array passed to function /test/, roughly that's
|
|
`A::value_type::value_type`.
|
|
|
|
Parameter /a/ is a matrix of test data: and must be a standard library Sequence type,
|
|
that contains another Sequence type:
|
|
typically it will be a two dimensional instance of
|
|
[^boost::array]. Each row
|
|
of /a/ should contain all the parameters that are passed to the function
|
|
under test as well as the expected result.
|
|
|
|
Parameter /test_func/ is the function under test, it is invoked with each row
|
|
of test data in /a/. Typically type F1 is created with Boost.Lambda: see
|
|
the example below.
|
|
|
|
Parameter /expect_func/ is a functor that extracts the expected result
|
|
from a row of test data in /a/. Typically type F2 is created with Boost.Lambda: see
|
|
the example below.
|
|
|
|
If the function under test returns a non-finite value when a finite result is
|
|
expected, or if a gross error is found, then a message is sent to `std::cerr`,
|
|
and a call to BOOST_ERROR() made (which means that including this header requires
|
|
you use Boost.Test). This is mainly a debugging/development aid
|
|
(and a good place for a breakpoint).
|
|
|
|
[h4 Example]
|
|
|
|
Suppose we want to test the `tgamma` and `lgamma` functions, we can create a
|
|
two-dimensional matrix of test data, each row is one test case, and contains
|
|
three elements: the input value, and the expected results for the `tgamma` and
|
|
`lgamma` functions respectively.
|
|
|
|
static const boost::array<boost::array<TestType, 3>, NumberOfTests>
|
|
factorials = {
|
|
/* big array of test data goes here */
|
|
};
|
|
|
|
Now we can invoke the test function to test tgamma:
|
|
|
|
using namespace boost::math::tools;
|
|
using namespace boost::lambda;
|
|
|
|
// get a pointer to the function under test:
|
|
TestType (*funcp)(TestType) = boost::math::tgamma;
|
|
|
|
// declare something to hold the result:
|
|
test_result<TestType> result;
|
|
//
|
|
// and test tgamma against data:
|
|
//
|
|
result = test(
|
|
factorials,
|
|
bind(funcp, ret<TestType>(_1[0])), // calls tgamma with factorials[row][0]
|
|
ret<TestType>(_1[1]) // extracts the expected result from factorials[row][1]
|
|
);
|
|
//
|
|
// Print out some results:
|
|
//
|
|
std::cout << "The Mean was " << result.mean() << std::endl;
|
|
std::cout << "The worst error was " << (result.max)() << std::endl;
|
|
std::cout << "The worst error was at row " << result.worst_case() << std::endl;
|
|
//
|
|
// same again with lgamma this time:
|
|
//
|
|
funcp = boost::math::lgamma;
|
|
result = test(
|
|
factorials,
|
|
bind(funcp, ret<TestType>(_1[0])), // calls tgamma with factorials[row][0]
|
|
ret<TestType>(_1[2]) // extracts the expected result from factorials[row][2]
|
|
);
|
|
//
|
|
// etc ...
|
|
//
|
|
|
|
[endsect] [/section:error_test Relative Error and Testing]
|
|
|
|
[/
|
|
Copyright 2006 John Maddock and Paul A. Bristow.
|
|
Distributed under the Boost Software License, Version 1.0.
|
|
(See accompanying file LICENSE_1_0.txt or copy at
|
|
http://www.boost.org/LICENSE_1_0.txt).
|
|
]
|