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172 lines
6.9 KiB
C++
172 lines
6.9 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 <exception>
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// Weisstein, Eric W. "Bessel Function Zeros." From MathWorld--A Wolfram Web Resource.
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// http://mathworld.wolfram.com/BesselFunctionZeros.html
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// Test values can be calculated using [@wolframalpha.com WolframAplha]
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// See also http://dlmf.nist.gov/10.21
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//[bessel_errors_example_1
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/*`[h5 Error messages from 'bad' input]
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Another example demonstrates calculating zeros of the Bessel functions
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showing the error messages from 'bad' input is handled by throwing exceptions.
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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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#include <boost/math/special_functions/airy.hpp>
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//] [/bessel_errors_example_1]
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int main()
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{
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//[bessel_errors_example_2
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/*`[tip It is always wise to place all code using Boost.Math inside try'n'catch blocks;
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this will ensure that helpful error messages can be shown when exceptional conditions arise.]
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Examples below show messages from several 'bad' arguments that throw a `domain_error` exception.
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*/
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try
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{ // Try a zero order v.
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float dodgy_root = boost::math::cyl_bessel_j_zero(0.F, 0);
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std::cout << "boost::math::cyl_bessel_j_zero(0.F, 0) " << dodgy_root << std::endl;
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// Thrown exception Error in function boost::math::cyl_bessel_j_zero<double>(double, int):
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// Requested the 0'th zero of J0, but the rank must be > 0 !
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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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/*`[note The type shown in the error message is the type [*after promotion],
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using __precision_policy and __promotion_policy, from `float` to `double` in this case.]
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In this example the promotion goes:
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# Arguments are `float` and `int`.
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# Treat `int` "as if" it were a `double`, so arguments are `float` and `double`.
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# Common type is `double` - so that's the precision we want (and the type that will be returned).
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# Evaluate internally as `double` for full `float` precision.
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See full code for other examples that promote from `double` to `long double`.
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Other examples of 'bad' inputs like infinity and NaN are below.
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Some compiler warnings indicate that 'bad' values are detected at compile time.
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*/
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try
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{ // order v = inf
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std::cout << "boost::math::cyl_bessel_j_zero(inf, 1) " << std::endl;
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double inf = std::numeric_limits<double>::infinity();
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double inf_root = boost::math::cyl_bessel_j_zero(inf, 1);
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std::cout << "boost::math::cyl_bessel_j_zero(inf, 1) " << inf_root << std::endl;
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// Throw exception Error in function boost::math::cyl_bessel_j_zero<long double>(long double, unsigned):
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// Order argument is 1.#INF, but must be finite >= 0 !
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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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try
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{ // order v = NaN, rank m = 1
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std::cout << "boost::math::cyl_bessel_j_zero(nan, 1) " << std::endl;
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double nan = std::numeric_limits<double>::quiet_NaN();
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double nan_root = boost::math::cyl_bessel_j_zero(nan, 1);
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std::cout << "boost::math::cyl_bessel_j_zero(nan, 1) " << nan_root << std::endl;
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// Throw exception Error in function boost::math::cyl_bessel_j_zero<long double>(long double, unsigned):
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// Order argument is 1.#QNAN, but must be finite >= 0 !
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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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/*`The output from other examples are shown appended to the full code listing.
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*/
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//] [/bessel_errors_example_2]
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try
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{ // Try a zero rank m.
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std::cout << "boost::math::cyl_neumann_zero(0.0, 0) " << std::endl;
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double dodgy_root = boost::math::cyl_bessel_j_zero(0.0, 0);
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// warning C4146: unary minus operator applied to unsigned type, result still unsigned.
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std::cout << "boost::math::cyl_neumann_zero(0.0, -1) " << dodgy_root << std::endl;
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// boost::math::cyl_neumann_zero(0.0, -1) 6.74652e+009
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// This *should* fail because m is unreasonably large.
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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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try
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{ // m = inf
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std::cout << "boost::math::cyl_bessel_j_zero(0.0, inf) " << std::endl;
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double inf = std::numeric_limits<double>::infinity();
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double inf_root = boost::math::cyl_bessel_j_zero(0.0, inf);
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// warning C4244: 'argument' : conversion from 'double' to 'int', possible loss of data.
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std::cout << "boost::math::cyl_bessel_j_zero(0.0, inf) " << inf_root << std::endl;
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// Throw exception Error in function boost::math::cyl_bessel_j_zero<long double>(long double, int):
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// Requested the 0'th zero, but must be > 0 !
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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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try
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{ // m = NaN
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double nan = std::numeric_limits<double>::quiet_NaN();
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double nan_root = boost::math::airy_ai_zero<double>(nan);
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// warning C4244: 'argument' : conversion from 'double' to 'int', possible loss of data.
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std::cout << "boost::math::airy_ai_zero<double>(nan) " << nan_root << std::endl;
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// Thrown exception Error in function boost::math::airy_ai_zero<double>(double,double):
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// The requested rank of the zero is 0, but must be 1 or more !
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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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} // int main()
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/*
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Output:
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Description: Autorun "J:\Cpp\big_number\Debug\bessel_errors_example.exe"
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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 !
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boost::math::cyl_bessel_j_zero(inf, 1)
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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 !
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boost::math::cyl_bessel_j_zero(nan, 1)
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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 !
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boost::math::cyl_neumann_zero(0.0, 0)
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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 !
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boost::math::cyl_bessel_j_zero(0.0, inf)
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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 !
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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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*/
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