ceph/src/boost/libs/math/doc/internals/relative_error.qbk

   1 [section:error_test Relative Error and Testing]
   2
   3 [h4 Synopsis]
   4
   5 ``
   6 #include <boost/math/tools/test.hpp>
   7 ``
   8
   9 [important
  10 The header `boost/math/tools/test.hpp` is located under `libs/math/include_private`
  11 and is not installed to the usual locations by default, you will need to add `libs/math/include_private`
  12 to your compiler's include path in order to use this header.]
  13
  14    template <class T>
  15    T relative_error(T a, T b);
  16
  17    template <class A, class F1, class F2>
  18    test_result<see-below> test(const A& a, F1 test_func, F2 expect_func);
  19
  20 [h4 Description]
  21
  22    template <class T>
  23    T relative_error(T a, T v);
  24
  25 Returns the relative error between /a/ and /v/ using the usual formula:
  26
  27 [equation error1]
  28
  29 In addition the value returned is zero if:
  30
  31 * Both /a/ and /v/ are infinite.
  32 * Both /a/ and /v/ are denormalised numbers or zero.
  33
  34 Otherwise if only one of /a/ and /v/ is zero then the value returned is 1.
  35
  36    template <class A, class F1, class F2>
  37    test_result<see-below> test(const A& a, F1 test_func, F2 expect_func);
  38
  39 This function is used for testing a function against tabulated test data.
  40
  41 The return type contains statistical data on the relative errors (max, mean,
  42 variance, and the number of test cases etc), as well as the row of test data that
  43 caused the largest relative error.  Public members of type test_result are:
  44
  45 [variablelist
  46 [[`unsigned worst()const;`][Returns the row at which the worst error occurred.]]
  47 [[`T min()const;`][Returns the smallest relative error found.]]
  48 [[`T max()const;`][Returns the largest relative error found.]]
  49 [[`T mean()const;`][Returns the mean error found.]]
  50 [[`boost::uintmax_t count()const;`][Returns the number of test cases.]]
  51 [[`T variance()const;`][Returns the variance of the errors found.]]
  52 [[`T variance1()const;`][Returns the unbiased variance of the errors found.]]
  53 [[`T rms()const`][Returns the Root Mean Square, or quadratic mean of the errors.]]
  54 [[`test_result& operator+=(const test_result& t)`][Combines two test_result's into
  55 a single result.]]
  56 ]
  57
  58 The template parameter of test_result, is the same type as the values in the two
  59 dimensional array passed to function /test/, roughly that's
  60 `A::value_type::value_type`.
  61
  62 Parameter /a/ is a matrix of test data: and must be a standard library Sequence type,
  63 that contains another Sequence type:
  64 typically it will be a two dimensional instance of
  65 [^boost::array].  Each row
  66 of /a/ should contain all the parameters that are passed to the function
  67 under test as well as the expected result.
  68
  69 Parameter /test_func/ is the function under test, it is invoked with each row
  70 of test data in /a/.  Typically type F1 is created with Boost.Lambda: see
  71 the example below.
  72
  73 Parameter /expect_func/ is a functor that extracts the expected result
  74 from a row of test data in /a/.  Typically type F2 is created with Boost.Lambda: see
  75 the example below.
  76
  77 If the function under test returns a non-finite value when a finite result is
  78 expected, or if a gross error is found, then a message is sent to `std::cerr`,
  79 and a call to BOOST_ERROR() made (which means that including this header requires
  80 you use Boost.Test).  This is mainly a debugging/development aid
  81 (and a good place for a breakpoint).
  82
  83 [h4 Example]
  84
  85 Suppose we want to test the tgamma and lgamma functions, we can create a
  86 two dimensional matrix of test data, each row is one test case, and contains
  87 three elements: the input value, and the expected results for the tgamma and
  88 lgamma functions respectively.
  89
  90    static const boost::array<boost::array<TestType, 3>, NumberOfTests>
  91       factorials = {
  92          /* big array of test data goes here */
  93       };
  94
  95 Now we can invoke the test function to test tgamma:
  96
  97    using namespace boost::math::tools;
  98    using namespace boost::lambda;
  99
 100    // get a pointer to the function under test:
 101    TestType (*funcp)(TestType) = boost::math::tgamma;
 102
 103    // declare something to hold the result:
 104    test_result<TestType> result;
 105    //
 106    // and test tgamma against data:
 107    //
 108    result = test(
 109       factorials,
 110       bind(funcp, ret<TestType>(_1[0])), // calls tgamma with factorials[row][0]
 111       ret<TestType>(_1[1])               // extracts the expected result from factorials[row][1]
 112    );
 113    //
 114    // Print out some results:
 115    //
 116    std::cout << "The Mean was " << result.mean() << std::endl;
 117    std::cout << "The worst error was " << (result.max)() << std::endl;
 118    std::cout << "The worst error was at row " << result.worst_case() << std::endl;
 119    //
 120    // same again with lgamma this time:
 121    //
 122    funcp = boost::math::lgamma;
 123    result = test(
 124       factorials,
 125       bind(funcp, ret<TestType>(_1[0])), // calls tgamma with factorials[row][0]
 126       ret<TestType>(_1[2])               // extracts the expected result from factorials[row][2]
 127    );
 128    //
 129    // etc ...
 130    //
 131
 132 [endsect][/section:error_test Relative Error and Testing]
 133
 134 [/
 135   Copyright 2006 John Maddock and Paul A. Bristow.
 136   Distributed under the Boost Software License, Version 1.0.
 137   (See accompanying file LICENSE_1_0.txt or copy at
 138   http://www.boost.org/LICENSE_1_0.txt).
 139 ]