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authorTavian Barnes <tavianator@gmail.com>2010-10-06 21:50:48 -0400
committerTavian Barnes <tavianator@gmail.com>2010-10-06 21:50:48 -0400
commitf1983adb487bb531c1c68226596b26eebf99876a (patch)
treec0700c79531e598b827d13a46eff18a3a6153967 /src/vZ/Adaptive.hpp
parentd5639168232d1c111d6924b10c6abd74204abec1 (diff)
downloadvz-f1983adb487bb531c1c68226596b26eebf99876a.tar.xz
Add Heun-Euler adaptive method.
Diffstat (limited to 'src/vZ/Adaptive.hpp')
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1 files changed, 109 insertions, 0 deletions
diff --git a/src/vZ/Adaptive.hpp b/src/vZ/Adaptive.hpp
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+/*************************************************************************
+ * Copyright (C) 2009-2010 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& 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; }
+
+ 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)
+ : GenericRKIntegrator<Y>(f), m_order(order),
+ m_a(a), m_b(b), m_bStar(bStar)
+ { }
+ virtual ~GenericAdaptiveIntegrator() { }
+
+ void step();
+
+ private:
+ Scalar m_atol, m_rtol;
+ unsigned int m_order;
+ ACoefficients m_a;
+ BCoefficients m_b, m_bStar;
+ };
+
+ // Type alias
+ typedef GenericAdaptiveIntegrator<double> AdaptiveIntegrator;
+
+ // Implementations
+
+ template <typename Y>
+ void
+ GenericAdaptiveIntegrator<Y>::step()
+ {
+ static const Scalar S = Scalar(19)/Scalar(20); // Arbitrary saftey factor
+ Scalar newH;
+ Y y;
+
+ // Attempt the integration step in a loop
+ bool rejected = true;
+ while (rejected) {
+ KVector 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);
+ 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);
+ } else {
+ rejected = false;
+ }
+ }
+
+ // Update x and y
+ this->y(y);
+ this->x(this->x() + this->h());
+
+ // Adjust the stepsize for the next iteration
+ this->h(newH);
+ }
+}
+
+#endif // VZ_ADAPTIVE_HPP