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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 <exception>
- // 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
- //[bessel_errors_example_1
- /*`[h5 Error messages from 'bad' input]
- Another example demonstrates calculating zeros of the Bessel functions
- showing the error messages from 'bad' input is handled by throwing exceptions.
- To use the functions for finding zeros of the functions we need:
- */
- #include <boost/math/special_functions/bessel.hpp>
- #include <boost/math/special_functions/airy.hpp>
- //] [/bessel_errors_example_1]
- int main()
- {
- //[bessel_errors_example_2
- /*`[tip It is always wise to place all code using Boost.Math inside try'n'catch blocks;
- this will ensure that helpful error messages can be shown when exceptional conditions arise.]
- Examples below show messages from several 'bad' arguments that throw a `domain_error` exception.
- */
- try
- { // Try a zero order v.
- float dodgy_root = boost::math::cyl_bessel_j_zero(0.F, 0);
- std::cout << "boost::math::cyl_bessel_j_zero(0.F, 0) " << dodgy_root << std::endl;
- // Thrown exception Error in function boost::math::cyl_bessel_j_zero<double>(double, int):
- // Requested the 0'th zero of J0, but the rank must be > 0 !
- }
- catch (std::exception& ex)
- {
- std::cout << "Thrown exception " << ex.what() << std::endl;
- }
- /*`[note The type shown in the error message is the type [*after promotion],
- using __precision_policy and __promotion_policy, from `float` to `double` in this case.]
- In this example the promotion goes:
- # Arguments are `float` and `int`.
- # Treat `int` "as if" it were a `double`, so arguments are `float` and `double`.
- # Common type is `double` - so that's the precision we want (and the type that will be returned).
- # Evaluate internally as `double` for full `float` precision.
- See full code for other examples that promote from `double` to `long double`.
- Other examples of 'bad' inputs like infinity and NaN are below.
- Some compiler warnings indicate that 'bad' values are detected at compile time.
- */
- try
- { // order v = inf
- std::cout << "boost::math::cyl_bessel_j_zero(inf, 1) " << std::endl;
- double inf = std::numeric_limits<double>::infinity();
- double inf_root = boost::math::cyl_bessel_j_zero(inf, 1);
- std::cout << "boost::math::cyl_bessel_j_zero(inf, 1) " << inf_root << std::endl;
- // Throw exception Error in function boost::math::cyl_bessel_j_zero<long double>(long double, unsigned):
- // Order argument is 1.#INF, but must be finite >= 0 !
- }
- catch (std::exception& ex)
- {
- std::cout << "Thrown exception " << ex.what() << std::endl;
- }
- try
- { // order v = NaN, rank m = 1
- std::cout << "boost::math::cyl_bessel_j_zero(nan, 1) " << std::endl;
- double nan = std::numeric_limits<double>::quiet_NaN();
- double nan_root = boost::math::cyl_bessel_j_zero(nan, 1);
- std::cout << "boost::math::cyl_bessel_j_zero(nan, 1) " << nan_root << std::endl;
- // Throw exception Error in function boost::math::cyl_bessel_j_zero<long double>(long double, unsigned):
- // Order argument is 1.#QNAN, but must be finite >= 0 !
- }
- catch (std::exception& ex)
- {
- std::cout << "Thrown exception " << ex.what() << std::endl;
- }
- /*`The output from other examples are shown appended to the full code listing.
- */
- //] [/bessel_errors_example_2]
- try
- { // Try a zero rank m.
- std::cout << "boost::math::cyl_neumann_zero(0.0, 0) " << std::endl;
- double dodgy_root = boost::math::cyl_bessel_j_zero(0.0, 0);
- // warning C4146: unary minus operator applied to unsigned type, result still unsigned.
- std::cout << "boost::math::cyl_neumann_zero(0.0, -1) " << dodgy_root << std::endl;
- // boost::math::cyl_neumann_zero(0.0, -1) 6.74652e+009
- // This *should* fail because m is unreasonably large.
- }
- catch (std::exception& ex)
- {
- std::cout << "Thrown exception " << ex.what() << std::endl;
- }
- try
- { // m = inf
- std::cout << "boost::math::cyl_bessel_j_zero(0.0, inf) " << std::endl;
- double inf = std::numeric_limits<double>::infinity();
- double inf_root = boost::math::cyl_bessel_j_zero(0.0, inf);
- // warning C4244: 'argument' : conversion from 'double' to 'int', possible loss of data.
- std::cout << "boost::math::cyl_bessel_j_zero(0.0, inf) " << inf_root << std::endl;
- // Throw exception Error in function boost::math::cyl_bessel_j_zero<long double>(long double, int):
- // Requested the 0'th zero, but must be > 0 !
- }
- catch (std::exception& ex)
- {
- std::cout << "Thrown exception " << ex.what() << std::endl;
- }
- try
- { // m = NaN
- double nan = std::numeric_limits<double>::quiet_NaN();
- double nan_root = boost::math::airy_ai_zero<double>(nan);
- // warning C4244: 'argument' : conversion from 'double' to 'int', possible loss of data.
- std::cout << "boost::math::airy_ai_zero<double>(nan) " << nan_root << std::endl;
- // Thrown exception Error in function boost::math::airy_ai_zero<double>(double,double):
- // The requested rank of the zero is 0, but must be 1 or more !
- }
- catch (std::exception& ex)
- {
- std::cout << "Thrown exception " << ex.what() << std::endl;
- }
- } // int main()
- /*
- Output:
- Description: Autorun "J:\Cpp\big_number\Debug\bessel_errors_example.exe"
- Thrown exception Error in function boost::math::cyl_bessel_j_zero<double>(double, int): Requested the 0'th zero of J0, but the rank must be > 0 !
- boost::math::cyl_bessel_j_zero(inf, 1)
- Thrown exception Error in function boost::math::cyl_bessel_j_zero<long double>(long double, int): Order argument is 1.#INF, but must be finite >= 0 !
- boost::math::cyl_bessel_j_zero(nan, 1)
- Thrown exception Error in function boost::math::cyl_bessel_j_zero<long double>(long double, int): Order argument is 1.#QNAN, but must be finite >= 0 !
- boost::math::cyl_neumann_zero(0.0, 0)
- Thrown exception Error in function boost::math::cyl_bessel_j_zero<long double>(long double, int): Requested the 0'th zero of J0, but the rank must be > 0 !
- boost::math::cyl_bessel_j_zero(0.0, inf)
- Thrown exception Error in function boost::math::cyl_bessel_j_zero<long double>(long double, int): Requested the -2147483648'th zero, but the rank must be positive !
- Thrown exception Error in function boost::math::airy_ai_zero<double>(double,double): The requested rank of the zero is 0, but must be 1 or more !
-
- */
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