1
2 // Copyright Christopher Kormanyos 2013.
3 // Copyright Paul A. Bristow 2013.
4 // Copyright John Maddock 2013.
5
6 // Distributed under the Boost Software License, Version 1.0.
7 // (See accompanying file LICENSE_1_0.txt or
8 // copy at http://www.boost.org/LICENSE_1_0.txt).
9
10 #ifdef _MSC_VER
11 # pragma warning (disable : 4512) // assignment operator could not be generated.
12 # pragma warning (disable : 4996) // assignment operator could not be generated.
13 #endif
14
15 #include <iostream>
16 #include <limits>
17 #include <vector>
18 #include <algorithm>
19 #include <iomanip>
20 #include <iterator>
21
22 //[neumann_zeros_example_1
23
24 /*`[h5 Calculating zeros of the Neumann function.]
25 This example also shows how Boost.Math and Boost.Multiprecision can be combined to provide
26 a many decimal digit precision. For 50 decimal digit precision we need to include
27 */
28
29 #include <boost/multiprecision/cpp_dec_float.hpp>
30
31 /*`and a `typedef` for `float_type` may be convenient
32 (allowing a quick switch to re-compute at built-in `double` or other precision)
33 */
34 typedef boost::multiprecision::cpp_dec_float_50 float_type;
35
36 //`To use the functions for finding zeros of the `cyl_neumann` function we need:
37
38 #include <boost/math/special_functions/bessel.hpp>
39 //] [/neumann_zerso_example_1]
40
main()41 int main()
42 {
43 try
44 {
45 {
46 //[neumann_zeros_example_2
47 /*`The Neumann (Bessel Y) function zeros are evaluated very similarly:
48 */
49 using boost::math::cyl_neumann_zero;
50 double zn = cyl_neumann_zero(2., 1);
51 std::cout << "cyl_neumann_zero(2., 1) = " << zn << std::endl;
52
53 std::vector<float> nzeros(3); // Space for 3 zeros.
54 cyl_neumann_zero<float>(2.F, 1, nzeros.size(), nzeros.begin());
55
56 std::cout << "cyl_neumann_zero<float>(2.F, 1, ";
57 // Print the zeros to the output stream.
58 std::copy(nzeros.begin(), nzeros.end(),
59 std::ostream_iterator<float>(std::cout, ", "));
60
61 std::cout << "\n""cyl_neumann_zero(static_cast<float_type>(220)/100, 1) = "
62 << cyl_neumann_zero(static_cast<float_type>(220)/100, 1) << std::endl;
63 // 3.6154383428745996706772556069431792744372398748422
64
65 //] //[/neumann_zeros_example_2]
66 }
67 }
68 catch (std::exception const& ex)
69 {
70 std::cout << "Thrown exception " << ex.what() << std::endl;
71 }
72 } // int main()
73
74 /*
75 Output:
76
77 cyl_neumann_zero(2., 1) = 3.38424
78 cyl_neumann_zero<float>(2.F, 1,
79 3.38424
80 6.79381
81 10.0235
82 3.61544
83 */
84
85
86