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/*************************************************************************
* Copyright (C) 2010 Tavian Barnes <tavianator@gmail.com> *
* *
* This file is part of The vZ Library. *
* *
* The vZ Library is free software; you can redistribute it and/or *
* modify it under the terms of the GNU Lesser General Public License as *
* published by the Free Software Foundation; either version 3 of the *
* License, or (at your option) any later version. *
* *
* The vZ Library is distributed in the hope that it will be useful, but *
* WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
* Lesser General Public License for more details. *
* *
* You should have received a copy of the GNU Lesser General Public *
* License along with this program. If not, see *
* <http://www.gnu.org/licenses/>. *
*************************************************************************/
#ifndef VZ_ADAPTIVE_HPP
#define VZ_ADAPTIVE_HPP
#include <cmath>
namespace vZ
{
// Base class for adaptive RK-style algorithms
template <typename Y>
class GenericAdaptiveIntegrator : public GenericRKIntegrator<Y>
{
public:
typedef typename GenericRKIntegrator<Y>::Scalar Scalar;
typedef typename GenericRKIntegrator<Y>::Function Function;
GenericAdaptiveIntegrator& tol(Scalar tol)
{ m_atol = tol; m_rtol = tol; return *this; }
GenericAdaptiveIntegrator& atol(Scalar tol) { m_atol = tol; return *this; }
GenericAdaptiveIntegrator& rtol(Scalar tol) { m_rtol = tol; return *this; }
Scalar atol() const { return m_atol; }
Scalar rtol() const { return m_rtol; }
unsigned int rejections() const { return m_rejections; }
protected:
typedef typename GenericRKIntegrator<Y>::ACoefficients ACoefficients;
typedef typename GenericRKIntegrator<Y>::BCoefficients BCoefficients;
typedef typename GenericRKIntegrator<Y>::KVector KVector;
GenericAdaptiveIntegrator(Function f, unsigned int order,
ACoefficients a, BCoefficients b,
BCoefficients bStar);
virtual ~GenericAdaptiveIntegrator() { }
void step();
private:
Scalar m_atol, m_rtol;
unsigned int m_order;
unsigned int m_rejections;
ACoefficients m_a;
BCoefficients m_b, m_bStar;
bool m_fsal, m_k1Set;
Y m_k1;
};
// Type alias
typedef GenericAdaptiveIntegrator<double> AdaptiveIntegrator;
// Implementations
template <typename Y>
GenericAdaptiveIntegrator<Y>::GenericAdaptiveIntegrator(
Function f, unsigned int order,
ACoefficients a, BCoefficients b, BCoefficients bStar
)
: GenericRKIntegrator<Y>(f), m_order(order), m_rejections(0),
m_a(a), m_b(b), m_bStar(bStar), m_fsal(true), m_k1Set(false)
{
std::size_t i;
for (i = 0; i < m_a.back().size(); ++i) {
if (m_a.back()[i] != m_b.at(i)) {
m_fsal = false;
return;
}
}
if (m_b.at(i) != Scalar(0))
m_fsal = false;
}
template <typename Y>
void
GenericAdaptiveIntegrator<Y>::step()
{
static const Scalar S = Scalar(19)/Scalar(20); // Arbitrary saftey factor
Scalar newH = this->h();
Y y;
KVector k;
// Attempt the integration step in a loop
while (true) {
if (m_k1Set) {
k = calculateK(m_k1, y, m_a);
} else if (m_fsal) {
k = calculateK(y, m_a);
} else {
k = calculateK(m_a);
y = calculateY(k, m_b);
}
Y yStar = calculateY(k, m_bStar);
// Get an error estimate
using std::abs;
using std::pow;
Scalar delta = abs(y - yStar);
if (delta == Scalar(0)) {
break;
}
Scalar scale = m_atol + std::max(abs(y), abs(this->y()))*m_rtol;
newH = S*this->h()*pow(scale/delta, Scalar(1)/m_order);
if (delta > scale) {
// Reject the step
this->h(newH);
++m_rejections;
} else {
break;
}
}
// Update x and y
this->y(y);
this->x(this->x() + this->h());
// Handle FSAL optimization
if (m_fsal) {
m_k1Set = true;
m_k1 = k.back();
}
// Adjust the stepsize for the next iteration
this->h(newH);
}
}
#endif // VZ_ADAPTIVE_HPP
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