test_spherical_harmonic.cpp

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//  (C) Copyright John Maddock 2006.
//  Use, modification and distribution are subject to 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)

#include <boost/math/concepts/real_concept.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/special_functions/spherical_harmonic.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/array.hpp>
#include "functor.hpp"

#include "handle_test_result.hpp"

//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the Spherical Harmonic Functions.
// There are two sets of tests, spot
// tests which compare our results with selected values computed
// using the online special function calculator at
// functions.wolfram.com, while the bulk of the accuracy tests
// use values generated with NTL::RR at 1000-bit precision
// and our generic versions of these functions.
//
// Note that when this file is first run on a new platform many of
// these tests will fail: the default accuracy is 1 epsilon which
// is too tight for most platforms.  In this situation you will
// need to cast a human eye over the error rates reported and make
// a judgement as to whether they are acceptable.  Either way please
// report the results to the Boost mailing list.  Acceptable rates of
// error are marked up below as a series of regular expressions that
// identify the compiler/stdlib/platform/data-type/test-data/test-function
// along with the maximum expected peek and RMS mean errors for that
// test.
//

void expected_results()
{
   //
   // Define the max and mean errors expected for
   // various compilers and platforms.
   //
   const char* largest_type;
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
   if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
   {
      largest_type = "(long\\s+)?double";
   }
   else
   {
      largest_type = "long double";
   }
#else
   largest_type = "(long\\s+)?double";
#endif
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
   if((std::numeric_limits<long double>::digits <= 64) &&
      (std::numeric_limits<long double>::digits != std::numeric_limits<double>::digits))
   {
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         "double",                      // test type(s)
         ".*",                          // test data group
         ".*", 10, 5);                  // test function
   }
#endif
   //
   // Catch all cases come last:
   //
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                  // test type(s)
      ".*",      // test data group
      ".*", 30000, 1000);  // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      "real_concept",                  // test type(s)
      ".*",      // test data group
      ".*", 30000, 1000);  // test function
   //
   // Finish off by printing out the compiler/stdlib/platform names,
   // we do this to make it easier to mark up expected error rates.
   //
   std::cout << "Tests run with " << BOOST_COMPILER << ", "
      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}

template <class T>
void do_test_spherical_harmonic(const T& data, const char* type_name, const char* test_name)
{
   typedef typename T::value_type row_type;
   typedef typename row_type::value_type value_type;

   typedef value_type (*pg)(unsigned, int, value_type, value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
   pg funcp = boost::math::spherical_harmonic_r<value_type, value_type>;
#else
   pg funcp = boost::math::spherical_harmonic_r;
#endif

   boost::math::tools::test_result<value_type> result;

   std::cout << "Testing " << test_name << " with type " << type_name
      << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";

   //
   // test Spheric Harmonic against data:
   //
   result = boost::math::tools::test(
      data,
      bind_func_int2(funcp, 0, 1, 2, 3),
      extract_result(4));
   handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::spherical_harmonic_r", test_name);

#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
   funcp = boost::math::spherical_harmonic_i<value_type, value_type>;
#else
   funcp = boost::math::spherical_harmonic_i;
#endif
   //
   // test Spheric Harmonic against data:
   //
   result = boost::math::tools::test(
      data,
      bind_func_int2(funcp, 0, 1, 2, 3),
      extract_result(5));
   handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::spherical_harmonic_i", test_name);

   std::cout << std::endl;
}

template <class T>
void test_complex_spherical_harmonic(const T& data, const char* /* name */, boost::mpl::true_ const &)
{
   typedef typename T::value_type row_type;
   typedef typename row_type::value_type value_type;

   for(unsigned i = 0; i < sizeof(data) / sizeof(data[0]); ++i)
   {
      //
      // Sanity check that the complex version does the same thing as the real
      // and imaginary versions:
      //
      std::complex<value_type> r = boost::math::spherical_harmonic(
         boost::math::tools::real_cast<unsigned>(data[i][0]),
         boost::math::tools::real_cast<unsigned>(data[i][1]),
         data[i][2],
         data[i][3]);
      value_type re = boost::math::spherical_harmonic_r(