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-rw-r--r--src/vZ/Adaptive.hpp109
-rw-r--r--src/vZ/Euler.hpp6
-rw-r--r--src/vZ/HE12.hpp107
-rw-r--r--src/vZ/Heun.hpp2
-rw-r--r--src/vZ/Midpoint.hpp8
-rw-r--r--src/vZ/RK4.hpp12
-rw-r--r--src/vZ/Simple.hpp2
7 files changed, 230 insertions, 16 deletions
diff --git a/src/vZ/Adaptive.hpp b/src/vZ/Adaptive.hpp
new file mode 100644
index 0000000..864b038
--- /dev/null
+++ b/src/vZ/Adaptive.hpp
@@ -0,0 +1,109 @@
+/*************************************************************************
+ * 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
diff --git a/src/vZ/Euler.hpp b/src/vZ/Euler.hpp
index 56c5678..033da2e 100644
--- a/src/vZ/Euler.hpp
+++ b/src/vZ/Euler.hpp
@@ -29,9 +29,9 @@ namespace vZ
// First order
// Its tableau is:
//
- // 0|
- // -+-
- // |1
+ // 0 |
+ // --+--
+ // | 1
//
// y[n + 1] = y[n] + dt*f(y[n])
template <typename Y>
diff --git a/src/vZ/HE12.hpp b/src/vZ/HE12.hpp
new file mode 100644
index 0000000..0f7a299
--- /dev/null
+++ b/src/vZ/HE12.hpp
@@ -0,0 +1,107 @@
+/*************************************************************************
+ * 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_HE12_HPP
+#define VZ_HE12_HPP
+
+namespace vZ
+{
+ // Heun-Euler method
+ //
+ // Second-order with embedded first-order
+ // Its tableau is:
+ //
+ // 0 |
+ // 1 | 1
+ // --+---------
+ // | 1/2 1/2
+ // | 1 0
+ //
+ // k1 = dt*f(y[n])
+ // k2 = dt*f(y[n] + dt*k1)
+ // y[n + 1] = y[n] + 1/2*(k1 + k2)
+ template <typename Y>
+ class GenericHE12Integrator : public GenericAdaptiveIntegrator<Y>
+ {
+ public:
+ typedef typename GenericAdaptiveIntegrator<Y>::Scalar Scalar;
+ typedef typename GenericAdaptiveIntegrator<Y>::Function Function;
+
+ GenericHE12Integrator(Function f)
+ : GenericAdaptiveIntegrator<Y>(f, 2, s_a, s_b, s_bStar) { }
+ ~GenericHE12Integrator() { }
+
+ private:
+ typedef typename GenericAdaptiveIntegrator<Y>::ACoefficients ACoefficients;
+ typedef typename GenericAdaptiveIntegrator<Y>::BCoefficients BCoefficients;
+
+ static ACoefficients s_a;
+ static BCoefficients s_b;
+ static BCoefficients s_bStar;
+
+ static Scalar s_a2Arr[1];
+ static std::vector<Scalar> s_aArr[1];
+ static Scalar s_bArr[2];
+ static Scalar s_bStarArr[2];
+ };
+
+ // Type alias
+ typedef GenericHE12Integrator<double> HE12Integrator;
+
+ // Implementation
+
+ template <typename Y>
+ typename GenericHE12Integrator<Y>::Scalar
+ GenericHE12Integrator<Y>::s_a2Arr[1] = {
+ Scalar(1)
+ };
+
+ template <typename Y>
+ std::vector<typename GenericHE12Integrator<Y>::Scalar>
+ GenericHE12Integrator<Y>::s_aArr[1] = {
+ std::vector<Scalar>(s_a2Arr, s_a2Arr + 1)
+ };
+
+ template <typename Y>
+ typename GenericHE12Integrator<Y>::ACoefficients
+ GenericHE12Integrator<Y>::s_a(s_aArr, s_aArr + 1);
+
+ template <typename Y>
+ typename GenericHE12Integrator<Y>::Scalar
+ GenericHE12Integrator<Y>::s_bArr[2] = {
+ Scalar(1)/Scalar(2), Scalar(1)/Scalar(2)
+ };
+
+ template <typename Y>
+ typename GenericHE12Integrator<Y>::BCoefficients
+ GenericHE12Integrator<Y>::s_b(s_bArr, s_bArr + 2);
+
+ template <typename Y>
+ typename GenericHE12Integrator<Y>::Scalar
+ GenericHE12Integrator<Y>::s_bStarArr[2] = {
+ Scalar(1), Scalar(0)
+ };
+
+ template <typename Y>
+ typename GenericHE12Integrator<Y>::BCoefficients
+ GenericHE12Integrator<Y>::s_bStar(s_bStarArr, s_bStarArr + 2);
+}
+
+#endif // VZ_HE12_HPP
diff --git a/src/vZ/Heun.hpp b/src/vZ/Heun.hpp
index b70df9e..5e697af 100644
--- a/src/vZ/Heun.hpp
+++ b/src/vZ/Heun.hpp
@@ -32,7 +32,7 @@ namespace vZ
// 0 |
// 1 | 1
// --+---------
- // | 1/2 1/2
+ // | 1/2 1/2
//
// k1 = dt*f(y[n])
// k2 = dt*f(y[n] + dt*k1)
diff --git a/src/vZ/Midpoint.hpp b/src/vZ/Midpoint.hpp
index 2329457..a4bb906 100644
--- a/src/vZ/Midpoint.hpp
+++ b/src/vZ/Midpoint.hpp
@@ -29,10 +29,10 @@ namespace vZ
// Two function evaluations per step
// Its tableau is:
//
- // 0 |
- // 1/2|1/2
- // ---+-----
- // |0 1
+ // 0 |
+ // 1/2 | 1/2
+ // ----+------
+ // | 0 1
//
// k1 = dt*f(y[n])
// k2 = dt*f(y[n] + (dt/2)*k1)
diff --git a/src/vZ/RK4.hpp b/src/vZ/RK4.hpp
index fa50461..39fa306 100644
--- a/src/vZ/RK4.hpp
+++ b/src/vZ/RK4.hpp
@@ -29,12 +29,12 @@ namespace vZ
// Four function evaluations per step
// Its tableau is:
//
- // 0 |
- // 1/2|1/2
- // 1/2|0 1/2
- // 1 |0 0 1
- // ---+---------------
- // |1/6 1/3 1/3 1/6
+ // 0 |
+ // 1/2 | 1/2
+ // 1/2 | 0 1/2
+ // 1 | 0 0 1
+ // ----+----------------
+ // | 1/6 1/3 1/3 1/6
//
// k1 = dt*f(y[n])
// k2 = dt*f(y[n] + (dt/2)*k1)
diff --git a/src/vZ/Simple.hpp b/src/vZ/Simple.hpp
index 9d9be46..5e4f7f8 100644
--- a/src/vZ/Simple.hpp
+++ b/src/vZ/Simple.hpp
@@ -21,8 +21,6 @@
#ifndef VZ_SIMPLE_HPP
#define VZ_SIMPLE_HPP
-#include <vector>
-
namespace vZ
{
// Base class for non-adaptive RK-style algorithms
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-22 14:22:04 +0000