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libs/math/example/neumann_zeros_example_1.cpp

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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>
+
+//[neumann_zeros_example_1
+
+/*`[h5 Calculating zeros of the Neumann function.]
+This example 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 `cyl_neumann` function we need:
+
+  #include <boost/math/special_functions/bessel.hpp>
+//] [/neumann_zerso_example_1]
+
+int main()
+{
+  try
+  {
+    {
+//[neumann_zeros_example_2
+/*`The Neumann (Bessel Y) function zeros are evaluated very similarly:
+*/
+    using boost::math::cyl_neumann_zero;
+    double zn = cyl_neumann_zero(2., 1);
+    std::cout << "cyl_neumann_zero(2., 1) = " << zn << std::endl;
+
+    std::vector<float> nzeros(3); // Space for 3 zeros.
+    cyl_neumann_zero<float>(2.F, 1, nzeros.size(), nzeros.begin());
+
+    std::cout << "cyl_neumann_zero<float>(2.F, 1, ";
+    // Print the zeros to the output stream.
+    std::copy(nzeros.begin(), nzeros.end(),
+              std::ostream_iterator<float>(std::cout, ", "));
+
+    std::cout << "\n""cyl_neumann_zero(static_cast<float_type>(220)/100, 1) = " 
+      << cyl_neumann_zero(static_cast<float_type>(220)/100, 1) << std::endl;
+    // 3.6154383428745996706772556069431792744372398748422
+
+//] //[/neumann_zeros_example_2]
+    }
+  }
+  catch (std::exception ex)
+  {
+    std::cout << "Thrown exception " << ex.what() << std::endl;
+  }
+} // int main()
+
+/*
+ Output:
+
+cyl_neumann_zero(2., 1) = 3.38424
+cyl_neumann_zero<float>(2.F, 1,
+3.38424
+6.79381
+10.0235
+3.61544
+*/
+
+