整理

include/boost/numeric/odeint/stepper/detail/pid_step_adjuster.hpp

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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