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