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- // Copyright Christopher Kormanyos 2013.
- // Copyright Paul A. Bristow 2013.
- // Copyright John Maddock 2013.
- // 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).
- #ifdef _MSC_VER
- # pragma warning (disable : 4512) // assignment operator could not be generated.
- # pragma warning (disable : 4996) // assignment operator could not be generated.
- #endif
- #include <iostream>
- #include <limits>
- #include <vector>
- #include <algorithm>
- #include <iomanip>
- #include <iterator>
- // Weisstein, Eric W. "Bessel Function Zeros." From MathWorld--A Wolfram Web Resource.
- // http://mathworld.wolfram.com/BesselFunctionZeros.html
- // Test values can be calculated using [@wolframalpha.com WolframAplha]
- // See also http://dlmf.nist.gov/10.21
- //[airy_zeros_example_1
- /*`This example demonstrates calculating zeros of the Airy functions.
- It also shows how Boost.Math and Boost.Multiprecision can be combined to provide
- a many decimal digit precision. For 50 decimal digit precision we need to include
- */
- #include <boost/multiprecision/cpp_dec_float.hpp>
- /*`and a `typedef` for `float_type` may be convenient
- (allowing a quick switch to re-compute at built-in `double` or other precision)
- */
- typedef boost::multiprecision::cpp_dec_float_50 float_type;
- //`To use the functions for finding zeros of the functions we need
- #include <boost/math/special_functions/airy.hpp>
- /*`This example shows obtaining both a single zero of the Airy functions,
- and then placing multiple zeros into a container like `std::vector` by providing an iterator.
- The signature of the single-value Airy Ai function is:
- template <class T>
- T airy_ai_zero(unsigned m); // 1-based index of the zero.
- The signature of multiple zeros Airy Ai function is:
- template <class T, class OutputIterator>
- OutputIterator airy_ai_zero(
- unsigned start_index, // 1-based index of the zero.
- unsigned number_of_zeros, // How many zeros to generate.
- OutputIterator out_it); // Destination for zeros.
- There are also versions which allows control of the __policy_section for error handling and precision.
- template <class T, class OutputIterator, class Policy>
- OutputIterator airy_ai_zero(
- unsigned start_index, // 1-based index of the zero.
- unsigned number_of_zeros, // How many zeros to generate.
- OutputIterator out_it, // Destination for zeros.
- const Policy& pol); // Policy to use.
- */
- //] [/airy_zeros_example_1]
- int main()
- {
- try
- {
- //[airy_zeros_example_2
- /*`[tip It is always wise to place code using Boost.Math inside `try'n'catch` blocks;
- this will ensure that helpful error messages are shown when exceptional conditions arise.]
- First, evaluate a single Airy zero.
- The precision is controlled by the template parameter `T`,
- so this example has `double` precision, at least 15 but up to 17 decimal digits
- (for the common 64-bit double).
- */
- double aiz1 = boost::math::airy_ai_zero<double>(1);
- std::cout << "boost::math::airy_ai_zero<double>(1) = " << aiz1 << std::endl;
- double aiz2 = boost::math::airy_ai_zero<double>(2);
- std::cout << "boost::math::airy_ai_zero<double>(2) = " << aiz2 << std::endl;
- double biz3 = boost::math::airy_bi_zero<double>(3);
- std::cout << "boost::math::airy_bi_zero<double>(3) = " << biz3 << std::endl;
- /*`Other versions of `airy_ai_zero` and `airy_bi_zero`
- allow calculation of multiple zeros with one call,
- placing the results in a container, often `std::vector`.
- For example, generate and display the first five `double` roots
- [@http://mathworld.wolfram.com/AiryFunctionZeros.html Wolfram Airy Functions Zeros].
- */
- unsigned int n_roots = 5U;
- std::vector<double> roots;
- boost::math::airy_ai_zero<double>(1U, n_roots, std::back_inserter(roots));
- std::cout << "airy_ai_zeros:" << std::endl;
- std::copy(roots.begin(),
- roots.end(),
- std::ostream_iterator<double>(std::cout, "\n"));
- /*`The first few real roots of Ai(x) are approximately -2.33811, -4.08795, -5.52056, -6.7867144, -7.94413, -9.02265 ...
- Or we can use Boost.Multiprecision to generate 50 decimal digit roots.
- We set the precision of the output stream, and show trailing zeros to display a fixed 50 decimal digits.
- */
- std::cout.precision(std::numeric_limits<float_type>::digits10); // float_type has 50 decimal digits.
- std::cout << std::showpoint << std::endl; // Show trailing zeros too.
- unsigned int m = 1U;
- float_type r = boost::math::airy_ai_zero<float_type>(1U); // 1st root.
- std::cout << "boost::math::airy_bi_zero<float_type>(" << m << ") = " << r << std::endl;
- m = 2;
- r = boost::math::airy_ai_zero<float_type>(2U); // 2nd root.
- std::cout << "boost::math::airy_bi_zero<float_type>(" << m << ") = " << r << std::endl;
- m = 7U;
- r = boost::math::airy_bi_zero<float_type>(7U); // 7th root.
- std::cout << "boost::math::airy_bi_zero<float_type>(" << m << ") = " << r << std::endl;
- std::vector<float_type> zeros;
- boost::math::airy_ai_zero<float_type>(1U, 3, std::back_inserter(zeros));
- std::cout << "airy_ai_zeros:" << std::endl;
- // Print the roots to the output stream.
- std::copy(zeros.begin(), zeros.end(),
- std::ostream_iterator<float_type>(std::cout, "\n"));
- //] [/airy_zeros_example_2]
- }
- catch (std::exception ex)
- {
- std::cout << "Thrown exception " << ex.what() << std::endl;
- }
- } // int main()
- /*
- Output:
- Description: Autorun "J:\Cpp\big_number\Debug\airy_zeros_example.exe"
- boost::math::airy_ai_zero<double>(1) = -2.33811
- boost::math::airy_ai_zero<double>(2) = -4.08795
- boost::math::airy_bi_zero<double>(3) = -4.83074
- airy_ai_zeros:
- -2.33811
- -4.08795
- -5.52056
- -6.78671
- -7.94413
- boost::math::airy_bi_zero<float_type>(1) = -2.3381074104597670384891972524467354406385401456711
- boost::math::airy_bi_zero<float_type>(2) = -4.0879494441309706166369887014573910602247646991085
- boost::math::airy_bi_zero<float_type>(7) = -9.5381943793462388866329885451560196208390720763825
- airy_ai_zeros:
- -2.3381074104597670384891972524467354406385401456711
- -4.0879494441309706166369887014573910602247646991085
- -5.5205598280955510591298555129312935737972142806175
- */
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