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author | Daniel Baumann <daniel.baumann@progress-linux.org> | 2024-04-27 18:24:20 +0000 |
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committer | Daniel Baumann <daniel.baumann@progress-linux.org> | 2024-04-27 18:24:20 +0000 |
commit | 483eb2f56657e8e7f419ab1a4fab8dce9ade8609 (patch) | |
tree | e5d88d25d870d5dedacb6bbdbe2a966086a0a5cf /src/boost/libs/numeric/odeint/examples/multiprecision | |
parent | Initial commit. (diff) | |
download | ceph-upstream.tar.xz ceph-upstream.zip |
Adding upstream version 14.2.21.upstream/14.2.21upstream
Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>
Diffstat (limited to 'src/boost/libs/numeric/odeint/examples/multiprecision')
3 files changed, 165 insertions, 0 deletions
diff --git a/src/boost/libs/numeric/odeint/examples/multiprecision/Jamfile b/src/boost/libs/numeric/odeint/examples/multiprecision/Jamfile new file mode 100644 index 00000000..9708d434 --- /dev/null +++ b/src/boost/libs/numeric/odeint/examples/multiprecision/Jamfile @@ -0,0 +1,16 @@ +# Copyright 2011-2013 Mario Mulansky +# Copyright 2012 Karsten Ahnert +# 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) + + +project + : requirements + <define>BOOST_ALL_NO_LIB=1 + : + ; + + +exe lorenz_mp : lorenz_mp.cpp ; +exe cmp_precision : cmp_precision.cpp ; diff --git a/src/boost/libs/numeric/odeint/examples/multiprecision/cmp_precision.cpp b/src/boost/libs/numeric/odeint/examples/multiprecision/cmp_precision.cpp new file mode 100644 index 00000000..779b5e29 --- /dev/null +++ b/src/boost/libs/numeric/odeint/examples/multiprecision/cmp_precision.cpp @@ -0,0 +1,68 @@ +/* Boost libs/numeric/odeint/examples/multiprecision/cmp_precision.cpp + + Copyright 2013 Karsten Ahnert + Copyright 2013 Mario Mulansky + + example comparing double to multiprecision using Boost.Multiprecision + + 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) + */ + + +#include <iostream> +#include <boost/numeric/odeint.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace std; +using namespace boost::numeric::odeint; + +typedef boost::multiprecision::cpp_dec_float_50 mp_50; + +/* we solve the simple ODE x' = 3/(2t^2) + x/(2t) + * with initial condition x(1) = 0. + * Analytic solution is x(t) = sqrt(t) - 1/t + */ + +void rhs_m( const mp_50 x , mp_50 &dxdt , const mp_50 t ) +{ // version for multiprecision + dxdt = mp_50(3)/(mp_50(2)*t*t) + x/(mp_50(2)*t); +} + +void rhs_d( const double x , double &dxdt , const double t ) +{ // version for double precision + dxdt = 3.0/(2.0*t*t) + x/(2.0*t); +} + +// state_type = mp_50 = deriv_type = time_type = mp_50 +typedef runge_kutta4< mp_50 , mp_50 , mp_50 , mp_50 , vector_space_algebra , default_operations , never_resizer > stepper_type_m; + +typedef runge_kutta4< double , double , double , double , vector_space_algebra , default_operations , never_resizer > stepper_type_d; + +int main() +{ + + stepper_type_m stepper_m; + stepper_type_d stepper_d; + + mp_50 dt_m( 0.5 ); + double dt_d( 0.5 ); + + cout << "dt" << '\t' << "mp" << '\t' << "double" << endl; + + while( dt_m > 1E-20 ) + { + + mp_50 x_m = 0; //initial value x(1) = 0 + stepper_m.do_step( rhs_m , x_m , mp_50( 1 ) , dt_m ); + double x_d = 0; + stepper_d.do_step( rhs_d , x_d , 1.0 , dt_d ); + + cout << dt_m << '\t'; + cout << abs((x_m - (sqrt(1+dt_m)-mp_50(1)/(1+dt_m)))/x_m) << '\t' ; + cout << abs((x_d - (sqrt(1+dt_d)-mp_50(1)/(1+dt_d)))/x_d) << endl ; + dt_m /= 2; + dt_d /= 2; + } +} diff --git a/src/boost/libs/numeric/odeint/examples/multiprecision/lorenz_mp.cpp b/src/boost/libs/numeric/odeint/examples/multiprecision/lorenz_mp.cpp new file mode 100644 index 00000000..c3e5b82e --- /dev/null +++ b/src/boost/libs/numeric/odeint/examples/multiprecision/lorenz_mp.cpp @@ -0,0 +1,81 @@ +/* + * lorenz_mp.cpp + * + * This example demonstrates how odeint can be used with boost.multiprecision. + * + * Copyright 2011-2012 Karsten Ahnert + * Copyright 2013 Mario Mulansky + * + * 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) + */ + + + +#include <iostream> + +//[ mp_lorenz_defs +#include <boost/numeric/odeint.hpp> +#include <boost/multiprecision/cpp_dec_float.hpp> + +using namespace std; +using namespace boost::numeric::odeint; + +typedef boost::multiprecision::cpp_dec_float_50 value_type; + +typedef boost::array< value_type , 3 > state_type; +//] + +//[ mp_lorenz_rhs +struct lorenz +{ + void operator()( const state_type &x , state_type &dxdt , value_type t ) const + { + const value_type sigma( 10 ); + const value_type R( 28 ); + const value_type b( value_type( 8 ) / value_type( 3 ) ); + + dxdt[0] = sigma * ( x[1] - x[0] ); + dxdt[1] = R * x[0] - x[1] - x[0] * x[2]; + dxdt[2] = -b * x[2] + x[0] * x[1]; + } +}; +//] + + + + +struct streaming_observer +{ + std::ostream& m_out; + + streaming_observer( std::ostream &out ) : m_out( out ) { } + + template< class State , class Time > + void operator()( const State &x , Time t ) const + { + m_out << t; + for( size_t i=0 ; i<x.size() ; ++i ) m_out << "\t" << x[i] ; + m_out << "\n"; + } +}; + + + + + + +int main( int argc , char **argv ) +{ + //[ mp_lorenz_int + state_type x = {{ value_type( 10.0 ) , value_type( 10.0 ) , value_type( 10.0 ) }}; + + cout.precision( 50 ); + integrate_const( runge_kutta4< state_type , value_type >() , + lorenz() , x , value_type( 0.0 ) , value_type( 10.0 ) , value_type( value_type( 1.0 ) / value_type( 10.0 ) ) , + streaming_observer( cout ) ); + //] + + return 0; +} |