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- /*
- boost/numeric/odeint/stepper/detail/pid_step_adjuster.hpp
- [begin_description]
- Implementation of the stepsize controller for the controlled adams bashforth moulton stepper.
- [end_description]
- Copyright 2017 Valentin Noah Hartmann
- 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)
- */
- #ifndef BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_PID_STEP_ADJUSTER_HPP_INCLUDED
- #define BOOST_NUMERIC_ODEINT_STEPPER_DETAIL_PID_STEP_ADJUSTER_HPP_INCLUDED
- #include <boost/numeric/odeint/stepper/detail/rotating_buffer.hpp>
- #include <boost/numeric/odeint/stepper/detail/pid_step_adjuster_coefficients.hpp>
- #include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
- #include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
- #include <math.h>
- namespace boost {
- namespace numeric {
- namespace odeint {
- namespace detail {
- template<
- class Value = double,
- class Time = double
- >
- struct pid_op
- {
- public:
- typedef Value value_type;
- typedef Time time_type;
- const double beta1;
- const double beta2;
- const double beta3;
- const double alpha1;
- const double alpha2;
- const time_type dt1;
- const time_type dt2;
- const time_type dt3;
- const size_t m_steps;
- pid_op(const size_t steps, const double _dt1, const double _dt2, const double _dt3,
- const double b1 = 1, const double b2 = 0, const double b3 = 0, const double a1 = 0, const double a2 = 0)
- :beta1(b1), beta2(b2), beta3(b3), alpha1(a1), alpha2(a2),
- dt1(_dt1), dt2(_dt2), dt3(_dt3),
- m_steps(steps)
- {};
- template<class T1, class T2, class T3, class T4>
- void operator()(T1 &t1, const T2 &t2, const T3 &t3, const T4 &t4)
- {
- using std::abs;
- t1 = adapted_pow(abs(t2), -beta1/(m_steps + 1)) *
- adapted_pow(abs(t3), -beta2/(m_steps + 1)) *
- adapted_pow(abs(t4), -beta3/(m_steps + 1)) *
- adapted_pow(abs(dt1/dt2), -alpha1/(m_steps + 1))*
- adapted_pow(abs(dt2/dt3), -alpha2/(m_steps + 1));
- t1 = 1/t1;
- };
- template<class T1, class T2>
- void operator()(T1 &t1, const T2 &t2)
- {
- using std::abs;
- t1 = adapted_pow(abs(t2), -beta1/(m_steps + 1));
- t1 = 1/t1;
- };
- private:
- template<class T>
- inline value_type adapted_pow(T base, double exp)
- {
- if(exp == 0)
- {
- return 1;
- }
- else if (exp > 0)
- {
- return pow(base, exp);
- }
- else
- {
- return 1/pow(base, -exp);
- }
- };
- };
- template<
- class State,
- class Value = double,
- class Deriv = State,
- class Time = double,
- class Algebra = typename algebra_dispatcher< State >::algebra_type,
- class Operations = typename operations_dispatcher< Deriv >::operations_type,
- size_t Type = BASIC
- >
- struct pid_step_adjuster
- {
- public:
- static double threshold() { return 0.9; };
- typedef State state_type;
- typedef Value value_type;
- typedef Deriv deriv_type;
- typedef Time time_type;
- typedef Algebra algebra_type;
- typedef Operations operations_type;
- typedef rotating_buffer<state_type, 3> error_storage_type;
- typedef rotating_buffer<time_type, 3> time_storage_type;
- typedef pid_step_adjuster_coefficients<Type> coeff_type;
- pid_step_adjuster(double abs_tol = 1e-6, double rel_tol = 1e-6, time_type dtmax = 1.0)
- :m_dtmax(dtmax), m_error_storage(), m_dt_storage(), m_init(0),
- m_abs_tol(abs_tol), m_rel_tol(rel_tol)
- {};
- time_type adjust_stepsize(const size_t steps, time_type dt, state_type &err, const state_type &x, const deriv_type &dxdt)
- {
- using std::abs;
- m_algebra.for_each3( err , x , dxdt ,
- typename operations_type::template rel_error< value_type >( m_abs_tol , m_rel_tol , 1.0 , 1.0 * abs(get_unit_value( dt )) ) );
- m_error_storage[0] = err;
- m_dt_storage[0] = dt;
- if(m_init >= 2)
- {
- m_algebra.for_each4(err, m_error_storage[0], m_error_storage[1], m_error_storage[2],
- pid_op<>(steps, m_dt_storage[0], m_dt_storage[1], m_dt_storage[2],
- m_coeff[0], m_coeff[1], m_coeff[2], m_coeff[3], m_coeff[4]));
- }
- else
- {
- m_algebra.for_each2(err, m_error_storage[0],
- pid_op<>(steps, m_dt_storage[0], m_dt_storage[1], m_dt_storage[2], 0.7));
- }
- value_type ratio = 1 / m_algebra.norm_inf(err);
- value_type kappa = 1.0;
- ratio = 1.0 + kappa*atan((ratio - 1) / kappa);
- if(ratio*dt >= m_dtmax)
- {
- ratio = m_dtmax / dt;
- }
- if(ratio >= threshold())
- {
- m_error_storage.rotate();
- m_dt_storage.rotate();
- ++m_init;
- }
- else
- {
- m_init = 0;
- }
- return dt * static_cast<time_type>(ratio);
- };
- private:
- algebra_type m_algebra;
- time_type m_dtmax;
- error_storage_type m_error_storage;
- time_storage_type m_dt_storage;
- size_t m_init;
- double m_abs_tol;
- double m_rel_tol;
- coeff_type m_coeff;
- };
- } // detail
- } // odeint
- } // numeric
- } // boost
- #endif
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