为什么 odeint 在较新版本的 odeint 中失败?

Why does odeint fail with the newer versions of odeint?

本文关键字：odeint 失败 新版本 为什么      更新时间：2023-10-16

我在为新版本的boost而苦苦挣扎。我正在使用具有多重精度的odeint。以下一段代码可以使用 boost 版本 1.67.0 成功编译。但是，从 1.68.0 及更高版本开始，我无法再编译。在 1.68.0 版本中引入了复杂的多精度数字，我也想在我的代码中使用此数据类型。有人可以告诉我代码中的错误在哪里吗？

#include <iostream>
#include <boost/array.hpp>
#include <boost/numeric/odeint.hpp>
#include <boost/multiprecision/gmp.hpp>
using namespace std;
using namespace boost::numeric::odeint;
typedef boost::multiprecision::mpf_float_100 mpf;
typedef boost::array< mpf , 1 > state_type;
void rhs( const state_type &x , state_type &dxdt , const mpf t )
{
dxdt[0] = ( - x[0] * sin( t ) + 2.0 * tan( t ) ) * x[0];
}
void write_out( const state_type &x , const mpf t )
{
cout.precision(50);
cout << t << 't' << x[0] << endl;
}
int main()
{
bulirsch_stoer< state_type , mpf , state_type , mpf > stepper( 1E-20 , 0 , 0 , 0 );
state_type x;
mpf t = mpf("0.2");
mpf dt = mpf("0.01");
mpf t_end = mpf("1.5");
x[0] = 1.15;
integrate_adaptive( stepper , rhs , x , t , t_end , dt , write_out );
}

我正在研究openuse，使用icpc或g ++ 7.4.1编译。我收到的 icpc 错误消息很长。

icpc -lgmp -I/userdir/boost_1_71_0/ code.cpp
/userdir/boost_1_71_0/boost/numeric/odeint/algebra/detail/extract_value_type.hpp(47): error: class "boost::numeric::odeint::detail::extract_value_type<mpf, void>" has no member "type"
typedef typename extract_value_type< typename S::value_type >::type type;
^
detected during:
instantiation of class "boost::numeric::odeint::detail::extract_value_type<S, boost::enable_if<has_value_type<S, boost::mpl::bool_<false>>, void>::type> [with S=mpf]" at line 47
instantiation of class "boost::numeric::odeint::detail::extract_value_type<S, boost::enable_if<has_value_type<S, boost::mpl::bool_<false>>, void>::type> [with S=boost::array<mpf, 1UL>]" at line 28 of "/userdir/boost_1_71_0/boost/numeric/odeint/algebra/norm_result_type.hpp"
instantiation of class "boost::numeric::odeint::norm_result_type<S, Enabler> [with S=boost::array<mpf, 1UL>, Enabler=void]" at line 89 of "/userdir/boost_1_71_0/boost/numeric/odeint/stepper/controlled_runge_kutta.hpp"
instantiation of "boost::numeric::odeint::default_error_checker<Value, Algebra, Operations>::value_type boost::numeric::odeint::default_error_checker<Value, Algebra, Operations>::error(boost::numeric::odeint::default_error_checker<Value, Algebra, Operations>::algebra_type &, const State &, const Deriv &, Err &, Time) const [with Value=mpf, Algebra=boost::numeric::odeint::array_algebra, Operations=boost::numeric::odeint::default_operations, State=state_type, Deriv=state_type,
Err=state_type, Time=mpf]" at line 235 of "/userdir/boost_1_71_0/boost/numeric/odeint/stepper/bulirsch_stoer.hpp"
instantiation of "boost::numeric::odeint::controlled_step_result={boost::numeric::odeint::controlled_step_result} boost::numeric::odeint::bulirsch_stoer<State, Value, Deriv, Time, Algebra, Operations, Resizer>::try_step(System, const StateIn &, const DerivIn &, boost::numeric::odeint::bulirsch_stoer<State, Value, Deriv, Time, Algebra, Operations, Resizer>::time_type &, StateOut &, boost::numeric::odeint::bulirsch_stoer<State, Value, Deriv, Time, Algebra, Operations,
Resizer>::time_type &) [with State=state_type, Value=mpf, Deriv=state_type, Time=mpf, Algebra=boost::numeric::odeint::array_algebra, Operations=boost::numeric::odeint::default_operations, Resizer=boost::numeric::odeint::initially_resizer, System=void (*)(const state_type &, state_type &, mpf), StateIn=state_type, DerivIn=state_type, StateOut=state_type]" at line 156 of "/userdir/boost_1_71_0/boost/numeric/odeint/stepper/bulirsch_stoer.hpp"
instantiation of "boost::numeric::odeint::controlled_step_result={boost::numeric::odeint::controlled_step_result} boost::numeric::odeint::bulirsch_stoer<State, Value, Deriv, Time, Algebra, Operations, Resizer>::try_step(System, StateInOut &, const DerivIn &, boost::numeric::odeint::bulirsch_stoer<State, Value, Deriv, Time, Algebra, Operations, Resizer>::time_type &, boost::numeric::odeint::bulirsch_stoer<State, Value, Deriv, Time, Algebra, Operations, Resizer>::time_type &) [with
State=state_type, Value=mpf, Deriv=state_type, Time=mpf, Algebra=boost::numeric::odeint::array_algebra, Operations=boost::numeric::odeint::default_operations, Resizer=boost::numeric::odeint::initially_resizer, System=void (*)(const state_type &, state_type &, mpf), StateInOut=state_type, DerivIn=state_type]" at line 393 of "/userdir/boost_1_71_0/boost/numeric/odeint/stepper/bulirsch_stoer.hpp"
instantiation of "boost::numeric::odeint::controlled_step_result={boost::numeric::odeint::controlled_step_result} boost::numeric::odeint::bulirsch_stoer<State, Value, Deriv, Time, Algebra, Operations, Resizer>::try_step_v1(System, StateInOut &, boost::numeric::odeint::bulirsch_stoer<State, Value, Deriv, Time, Algebra, Operations, Resizer>::time_type &, boost::numeric::odeint::bulirsch_stoer<State, Value, Deriv, Time, Algebra, Operations, Resizer>::time_type &) [with State=state_type,
Value=mpf, Deriv=state_type, Time=mpf, Algebra=boost::numeric::odeint::array_algebra, Operations=boost::numeric::odeint::default_operations, Resizer=boost::numeric::odeint::initially_resizer, System=void (*)(const state_type &, state_type &, mpf), StateInOut=state_type]" at line 135 of "/userdir/boost_1_71_0/boost/numeric/odeint/stepper/bulirsch_stoer.hpp"
instantiation of "boost::numeric::odeint::controlled_step_result={boost::numeric::odeint::controlled_step_result} boost::numeric::odeint::bulirsch_stoer<State, Value, Deriv, Time, Algebra, Operations, Resizer>::try_step(System, StateInOut &, boost::numeric::odeint::bulirsch_stoer<State, Value, Deriv, Time, Algebra, Operations, Resizer>::time_type &, boost::numeric::odeint::bulirsch_stoer<State, Value, Deriv, Time, Algebra, Operations, Resizer>::time_type &) [with State=state_type,
Value=mpf, Deriv=state_type, Time=mpf, Algebra=boost::numeric::odeint::array_algebra, Operations=boost::numeric::odeint::default_operations, Resizer=boost::numeric::odeint::initially_resizer, System=void (*)(const state_type &, state_type &, mpf), StateInOut=state_type]" at line 103 of "/userdir/boost_1_71_0/boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp"
instantiation of "size_t={unsigned long} boost::numeric::odeint::detail::integrate_adaptive(Stepper, System, State &, Time &, Time, Time &, Observer, boost::numeric::odeint::controlled_stepper_tag) [with Stepper=boost::numeric::odeint::bulirsch_stoer<state_type, mpf, state_type, mpf, boost::numeric::odeint::array_algebra, boost::numeric::odeint::default_operations, boost::numeric::odeint::initially_resizer>, System=void (*)(const state_type &, state_type &, mpf), State=state_type,
Time=mpf, Observer=void (*)(const state_type &, mpf)]" at line 45 of "/userdir/boost_1_71_0/boost/numeric/odeint/integrate/integrate_adaptive.hpp"
instantiation of "size_t={unsigned long} boost::numeric::odeint::integrate_adaptive(Stepper, System, State &, Time, Time, Time, Observer) [with Stepper=boost::numeric::odeint::bulirsch_stoer<state_type, mpf, state_type, mpf, boost::numeric::odeint::array_algebra, boost::numeric::odeint::default_operations, boost::numeric::odeint::initially_resizer>, System=void (*)(const state_type &, state_type &, mpf), State=state_type, Time=mpf, Observer=void (*)(const state_type &, mpf)]" at line
36 of "code.cpp"
compilation aborted for code.cpp (code 2)

问题似乎是boost::multiprecision::number，是什么让mpf_float_100(以及所有其他 Boost.Multiprecision 类型(工作，自 Boost 1.68 以来具有相关的value_type，因此 Boost.Numeric.Odeint 将其视为容器，而事实并非如此。Odeint 检查类型是否为容器的方式是使用 trait：has_value_type，将该特征专门用于number应该有效：

#include <iostream>
#include <boost/array.hpp>
#include <boost/numeric/odeint.hpp>
#include <boost/multiprecision/gmp.hpp>
template< typename Backend, boost::multiprecision::expression_template_option Option >
struct has_value_type<boost::multiprecision::number<Backend,Option> >:boost::mpl::false_{}; //ADDED
using namespace std;
using namespace boost::numeric::odeint;
namespace mp=boost::multiprecision;
typedef boost::multiprecision::mpf_float_100 mpf;
typedef boost::array< mpf , 1 > state_type;
void rhs( const state_type &x , state_type &dxdt , const mpf t )
{
dxdt[0] = ( - x[0] * sin( t ) + 2.0 * tan( t ) ) * x[0];
}
void write_out( const state_type &x , const mpf t )
{
cout.precision(50);
cout << t << 't' << x[0] << endl;
}
int main()
{
bulirsch_stoer< state_type , mpf , state_type , mpf > stepper( 1E-20 , 0 , 0 , 0 );
state_type x;
mpf t = mpf("0.2");
mpf dt = mpf("0.01");
mpf t_end = mpf("1.5");
x[0] = 1.15;
integrate_adaptive( stepper , rhs , x , t , t_end , dt , write_out );
}
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