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89 lines
2.3 KiB
C++
89 lines
2.3 KiB
C++
// Copyright Christopher Kormanyos 2013.
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// Copyright Paul A. Bristow 2013.
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// Copyright John Maddock 2013.
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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
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// copy at http://www.boost.org/LICENSE_1_0.txt).
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#ifdef _MSC_VER
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# pragma warning (disable : 4512) // assignment operator could not be generated.
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# pragma warning (disable : 4996) // assignment operator could not be generated.
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#endif
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#include <iostream>
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#include <limits>
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#include <vector>
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#include <algorithm>
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#include <iomanip>
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#include <iterator>
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//[bessel_zeros_iterator_example_1
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/*`[h5 Using Output Iterator to sum zeros of Bessel Functions]
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This example demonstrates summing zeros of the Bessel functions.
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To use the functions for finding zeros of the functions we need
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*/
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#include <boost/math/special_functions/bessel.hpp>
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/*`We use the `cyl_bessel_j_zero` output iterator parameter `out_it`
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to create a sum of ['1/zeros[super 2]] by defining a custom output iterator:
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*/
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template <class T>
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struct output_summation_iterator
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{
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output_summation_iterator(T* p) : p_sum(p)
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{}
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output_summation_iterator& operator*()
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{ return *this; }
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output_summation_iterator& operator++()
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{ return *this; }
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output_summation_iterator& operator++(int)
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{ return *this; }
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output_summation_iterator& operator = (T const& val)
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{
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*p_sum += 1./ (val * val); // Summing 1/zero^2.
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return *this;
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}
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private:
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T* p_sum;
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};
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//] [/bessel_zeros_iterator_example_1]
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int main()
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{
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try
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{
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//[bessel_zeros_iterator_example_2
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/*`The sum is calculated for many values, converging on the analytical exact value of `1/8`.
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*/
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using boost::math::cyl_bessel_j_zero;
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double nu = 1.;
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double sum = 0;
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output_summation_iterator<double> it(&sum); // sum of 1/zeros^2
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cyl_bessel_j_zero(nu, 1, 10000, it);
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double s = 1/(4 * (nu + 1)); // 0.125 = 1/8 is exact analytical solution.
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std::cout << std::setprecision(6) << "nu = " << nu << ", sum = " << sum
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<< ", exact = " << s << std::endl;
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// nu = 1.00000, sum = 0.124990, exact = 0.125000
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//] [/bessel_zeros_iterator_example_2]
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}
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catch (std::exception ex)
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{
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std::cout << "Thrown exception " << ex.what() << std::endl;
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}
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return 0;
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} // int_main()
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/*
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Output:
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nu = 1, sum = 0.12499, exact = 0.125
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*/
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