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authorTavian Barnes <tavianator@gmail.com>2010-10-06 17:57:48 -0400
committerTavian Barnes <tavianator@gmail.com>2010-10-06 17:57:48 -0400
commit39617c503faf08de1324516adc8ebb7150c218ca (patch)
treea9219fe89fada63a6c42ad6d1546f129c1237497
parentfa85e866aa876a50e735e6d84f5fa32e52fb2f0b (diff)
downloadvz-39617c503faf08de1324516adc8ebb7150c218ca.tar.xz
Add RK4.
-rw-r--r--src/Makefile.am1
-rw-r--r--src/vZ.hpp1
-rw-r--r--src/vZ/Midpoint.hpp2
-rw-r--r--src/vZ/RK.hpp2
-rw-r--r--src/vZ/RK4.hpp116
-rw-r--r--tests/Makefile.am4
-rw-r--r--tests/RK4.cpp25
7 files changed, 148 insertions, 3 deletions
diff --git a/src/Makefile.am b/src/Makefile.am
index 6cd2924..ff03023 100644
--- a/src/Makefile.am
+++ b/src/Makefile.am
@@ -22,5 +22,6 @@ nobase_include_HEADERS = vZ.hpp \
vZ/Integrator.hpp \
vZ/Midpoint.hpp \
vZ/RK.hpp \
+ vZ/RK4.hpp \
vZ/Simple.hpp \
vZ/Traits.hpp
diff --git a/src/vZ.hpp b/src/vZ.hpp
index b25e615..9d47b33 100644
--- a/src/vZ.hpp
+++ b/src/vZ.hpp
@@ -29,5 +29,6 @@
#include <vZ/Simple.hpp>
#include <vZ/Euler.hpp>
#include <vZ/Midpoint.hpp>
+#include <vZ/RK4.hpp>
#endif // VZ_HPP
diff --git a/src/vZ/Midpoint.hpp b/src/vZ/Midpoint.hpp
index 3d7ce2c..2329457 100644
--- a/src/vZ/Midpoint.hpp
+++ b/src/vZ/Midpoint.hpp
@@ -68,7 +68,7 @@ namespace vZ
template <typename Y>
typename GenericMidpointIntegrator<Y>::Scalar
GenericMidpointIntegrator<Y>::s_a2Arr[1] = {
- Scalar(1)/2
+ Scalar(1)/Scalar(2)
};
template <typename Y>
diff --git a/src/vZ/RK.hpp b/src/vZ/RK.hpp
index df608ff..a832779 100644
--- a/src/vZ/RK.hpp
+++ b/src/vZ/RK.hpp
@@ -69,7 +69,7 @@ namespace vZ
i != a.end();
++i)
{
- Scalar c = 0;
+ Scalar c(0);
Y y = this->y();
for (typename std::vector<Scalar>::size_type j = 0; j < i->size(); ++j) {
Scalar aij = i->at(j);
diff --git a/src/vZ/RK4.hpp b/src/vZ/RK4.hpp
new file mode 100644
index 0000000..fa50461
--- /dev/null
+++ b/src/vZ/RK4.hpp
@@ -0,0 +1,116 @@
+/*************************************************************************
+ * 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_RK4_HPP
+#define VZ_RK4_HPP
+
+namespace vZ
+{
+ // RK4 method
+ //
+ // Fourth order Runge-Kutta method
+ // 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
+ //
+ // k1 = dt*f(y[n])
+ // k2 = dt*f(y[n] + (dt/2)*k1)
+ // k3 = dt*f(y[n] + (dt/2)*k2)
+ // k4 = dt*f(y[n] + dt*k3)
+ // y[n + 1] = y[n] + (k1 + 2*k2 + 2*k3 + k4)/6
+ template <typename Y>
+ class GenericRK4Integrator : public GenericSimpleIntegrator<Y>
+ {
+ public:
+ typedef typename GenericSimpleIntegrator<Y>::Scalar Scalar;
+ typedef typename GenericSimpleIntegrator<Y>::Function Function;
+
+ GenericRK4Integrator(Function f)
+ : GenericSimpleIntegrator<Y>(f, s_a, s_b) { }
+ ~GenericRK4Integrator() { }
+
+ private:
+ typedef typename GenericSimpleIntegrator<Y>::ACoefficients ACoefficients;
+ typedef typename GenericSimpleIntegrator<Y>::BCoefficients BCoefficients;
+
+ static ACoefficients s_a;
+ static BCoefficients s_b;
+
+ static Scalar s_a2Arr[1];
+ static Scalar s_a3Arr[2];
+ static Scalar s_a4Arr[3];
+ static std::vector<Scalar> s_aArr[3];
+ static Scalar s_bArr[4];
+ };
+
+ // Type alias
+ typedef GenericRK4Integrator<double> RK4Integrator;
+
+ // Implementation
+
+ template <typename Y>
+ typename GenericRK4Integrator<Y>::Scalar
+ GenericRK4Integrator<Y>::s_a2Arr[1] = {
+ Scalar(1)/Scalar(2)
+ };
+ template <typename Y>
+ typename GenericRK4Integrator<Y>::Scalar
+ GenericRK4Integrator<Y>::s_a3Arr[2] = {
+ Scalar(0), Scalar(1)/Scalar(2)
+ };
+ template <typename Y>
+ typename GenericRK4Integrator<Y>::Scalar
+ GenericRK4Integrator<Y>::s_a4Arr[3] = {
+ Scalar(0), Scalar(0), Scalar(1)
+ };
+
+ template <typename Y>
+ std::vector<typename GenericRK4Integrator<Y>::Scalar>
+ GenericRK4Integrator<Y>::s_aArr[3] = {
+ std::vector<Scalar>(s_a2Arr, s_a2Arr + 1),
+ std::vector<Scalar>(s_a3Arr, s_a3Arr + 2),
+ std::vector<Scalar>(s_a4Arr, s_a4Arr + 3)
+ };
+
+ template <typename Y>
+ typename GenericRK4Integrator<Y>::ACoefficients
+ GenericRK4Integrator<Y>::s_a(s_aArr, s_aArr + 3);
+
+ template <typename Y>
+ typename GenericRK4Integrator<Y>::Scalar
+ GenericRK4Integrator<Y>::s_bArr[4] = {
+ Scalar(1)/Scalar(6),
+ Scalar(1)/Scalar(3),
+ Scalar(1)/Scalar(3),
+ Scalar(1)/Scalar(6)
+ };
+
+ template <typename Y>
+ typename GenericRK4Integrator<Y>::BCoefficients
+ GenericRK4Integrator<Y>::s_b(s_bArr, s_bArr + 4);
+}
+
+#endif // VZ_RK4_HPP
diff --git a/tests/Makefile.am b/tests/Makefile.am
index 5f94aab..edef1ae 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -20,8 +20,10 @@
INCLUDES = -I$(top_srcdir)/src
check_PROGRAMS = Euler-test \
- Midpoint-test
+ Midpoint-test \
+ RK4-test
TESTS = $(check_PROGRAMS)
Euler_test_SOURCES = Euler.cpp
Midpoint_test_SOURCES = Midpoint.cpp
+RK4_test_SOURCES = RK4.cpp
diff --git a/tests/RK4.cpp b/tests/RK4.cpp
new file mode 100644
index 0000000..8e0ca0a
--- /dev/null
+++ b/tests/RK4.cpp
@@ -0,0 +1,25 @@
+#include "vZ.hpp"
+#include <cmath>
+#include <cstdlib>
+#include <iostream>
+
+// y' = y (y == C*exp(t))
+double
+f(double t, double y)
+{
+ return y;
+}
+
+int
+main()
+{
+ vZ::RK4Integrator integrator(f);
+ integrator.y(1.0).x(0.0).h(0.04);
+
+ integrator.integrate(2.0);
+
+ std::cout << integrator.y() << std::endl
+ << std::exp(2.0) << std::endl;
+
+ return EXIT_SUCCESS;
+}