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authorTavian Barnes <tavianator@gmail.com>2010-10-06 17:26:06 -0400
committerTavian Barnes <tavianator@gmail.com>2010-10-06 17:26:06 -0400
commitfa85e866aa876a50e735e6d84f5fa32e52fb2f0b (patch)
tree3758be8b09c812f936d07d8b58fb16e6996a80ef
parent0f04e97fa748b6740da4c9512b596d7d3a2788c5 (diff)
downloadvz-fa85e866aa876a50e735e6d84f5fa32e52fb2f0b.tar.xz
Add the midpoint method.
-rw-r--r--src/Makefile.am1
-rw-r--r--src/vZ.hpp1
-rw-r--r--src/vZ/Midpoint.hpp95
-rw-r--r--tests/Makefile.am6
-rw-r--r--tests/Midpoint.cpp25
5 files changed, 126 insertions, 2 deletions
diff --git a/src/Makefile.am b/src/Makefile.am
index 76c30b1..6cd2924 100644
--- a/src/Makefile.am
+++ b/src/Makefile.am
@@ -20,6 +20,7 @@
nobase_include_HEADERS = vZ.hpp \
vZ/Euler.hpp \
vZ/Integrator.hpp \
+ vZ/Midpoint.hpp \
vZ/RK.hpp \
vZ/Simple.hpp \
vZ/Traits.hpp
diff --git a/src/vZ.hpp b/src/vZ.hpp
index 12e4cbc..b25e615 100644
--- a/src/vZ.hpp
+++ b/src/vZ.hpp
@@ -28,5 +28,6 @@
#include <vZ/RK.hpp>
#include <vZ/Simple.hpp>
#include <vZ/Euler.hpp>
+#include <vZ/Midpoint.hpp>
#endif // VZ_HPP
diff --git a/src/vZ/Midpoint.hpp b/src/vZ/Midpoint.hpp
new file mode 100644
index 0000000..3d7ce2c
--- /dev/null
+++ b/src/vZ/Midpoint.hpp
@@ -0,0 +1,95 @@
+/*************************************************************************
+ * 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_MIDPOINT_HPP
+#define VZ_MIDPOINT_HPP
+
+namespace vZ
+{
+ // Midpoint method
+ //
+ // Second order Runge-Kutta method
+ // Two function evaluations per step
+ // Its tableau is:
+ //
+ // 0 |
+ // 1/2|1/2
+ // ---+-----
+ // |0 1
+ //
+ // k1 = dt*f(y[n])
+ // k2 = dt*f(y[n] + (dt/2)*k1)
+ // y[n + 1] = y[n] + k2
+ template <typename Y>
+ class GenericMidpointIntegrator : public GenericSimpleIntegrator<Y>
+ {
+ public:
+ typedef typename GenericSimpleIntegrator<Y>::Scalar Scalar;
+ typedef typename GenericSimpleIntegrator<Y>::Function Function;
+
+ GenericMidpointIntegrator(Function f)
+ : GenericSimpleIntegrator<Y>(f, s_a, s_b) { }
+ ~GenericMidpointIntegrator() { }
+
+ 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 std::vector<Scalar> s_aArr[1];
+ static Scalar s_bArr[2];
+ };
+
+ // Type alias
+ typedef GenericMidpointIntegrator<double> MidpointIntegrator;
+
+ // Implementation
+
+ template <typename Y>
+ typename GenericMidpointIntegrator<Y>::Scalar
+ GenericMidpointIntegrator<Y>::s_a2Arr[1] = {
+ Scalar(1)/2
+ };
+
+ template <typename Y>
+ std::vector<typename GenericMidpointIntegrator<Y>::Scalar>
+ GenericMidpointIntegrator<Y>::s_aArr[1] = {
+ std::vector<Scalar>(s_a2Arr, s_a2Arr + 1)
+ };
+
+ template <typename Y>
+ typename GenericMidpointIntegrator<Y>::ACoefficients
+ GenericMidpointIntegrator<Y>::s_a(s_aArr, s_aArr + 1);
+
+ template <typename Y>
+ typename GenericMidpointIntegrator<Y>::Scalar
+ GenericMidpointIntegrator<Y>::s_bArr[2] = {
+ Scalar(0), Scalar(1)
+ };
+
+ template <typename Y>
+ typename GenericMidpointIntegrator<Y>::BCoefficients
+ GenericMidpointIntegrator<Y>::s_b(s_bArr, s_bArr + 2);
+}
+
+#endif // VZ_MIDPOINT_HPP
diff --git a/tests/Makefile.am b/tests/Makefile.am
index a3d5a77..5f94aab 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -19,7 +19,9 @@
INCLUDES = -I$(top_srcdir)/src
-check_PROGRAMS = Euler-test
+check_PROGRAMS = Euler-test \
+ Midpoint-test
TESTS = $(check_PROGRAMS)
-Euler_test_SOURCES = Euler.cpp
+Euler_test_SOURCES = Euler.cpp
+Midpoint_test_SOURCES = Midpoint.cpp
diff --git a/tests/Midpoint.cpp b/tests/Midpoint.cpp
new file mode 100644
index 0000000..aea1885
--- /dev/null
+++ b/tests/Midpoint.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::MidpointIntegrator integrator(f);
+ integrator.y(1.0).x(0.0).h(0.02);
+
+ integrator.integrate(2.0);
+
+ std::cout << integrator.y() << std::endl
+ << std::exp(2.0) << std::endl;
+
+ return EXIT_SUCCESS;
+}