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Commons Math example source code file (ClassicalRungeKuttaIntegratorTest.java)
The Commons Math ClassicalRungeKuttaIntegratorTest.java source code/* * Licensed to the Apache Software Foundation (ASF) under one or more * contributor license agreements. See the NOTICE file distributed with * this work for additional information regarding copyright ownership. * The ASF licenses this file to You under the Apache License, Version 2.0 * (the "License"); you may not use this file except in compliance with * the License. You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package org.apache.commons.math.ode.nonstiff; import junit.framework.*; import org.apache.commons.math.ode.DerivativeException; import org.apache.commons.math.ode.FirstOrderDifferentialEquations; import org.apache.commons.math.ode.FirstOrderIntegrator; import org.apache.commons.math.ode.IntegratorException; import org.apache.commons.math.ode.TestProblem1; import org.apache.commons.math.ode.TestProblem3; import org.apache.commons.math.ode.TestProblem5; import org.apache.commons.math.ode.TestProblemAbstract; import org.apache.commons.math.ode.TestProblemFactory; import org.apache.commons.math.ode.TestProblemHandler; import org.apache.commons.math.ode.events.EventHandler; import org.apache.commons.math.ode.nonstiff.ClassicalRungeKuttaIntegrator; import org.apache.commons.math.ode.sampling.StepHandler; import org.apache.commons.math.ode.sampling.StepInterpolator; public class ClassicalRungeKuttaIntegratorTest extends TestCase { public ClassicalRungeKuttaIntegratorTest(String name) { super(name); } public void testMissedEndEvent() throws IntegratorException, DerivativeException { final double t0 = 1878250320.0000029; final double tEvent = 1878250379.9999986; final double[] k = { 1.0e-4, 1.0e-5, 1.0e-6 }; FirstOrderDifferentialEquations ode = new FirstOrderDifferentialEquations() { public int getDimension() { return k.length; } public void computeDerivatives(double t, double[] y, double[] yDot) { for (int i = 0; i < y.length; ++i) { yDot[i] = k[i] * y[i]; } } }; ClassicalRungeKuttaIntegrator integrator = new ClassicalRungeKuttaIntegrator(60.0); double[] y0 = new double[k.length]; for (int i = 0; i < y0.length; ++i) { y0[i] = i + 1; } double[] y = new double[k.length]; double finalT = integrator.integrate(ode, t0, y0, tEvent, y); Assert.assertEquals(tEvent, finalT, 5.0e-6); for (int i = 0; i < y.length; ++i) { Assert.assertEquals(y0[i] * Math.exp(k[i] * (finalT - t0)), y[i], 1.0e-9); } integrator.addEventHandler(new EventHandler() { public void resetState(double t, double[] y) { } public double g(double t, double[] y) { return t - tEvent; } public int eventOccurred(double t, double[] y, boolean increasing) { Assert.assertEquals(tEvent, t, 5.0e-6); return CONTINUE; } }, Double.POSITIVE_INFINITY, 1.0e-20, 100); finalT = integrator.integrate(ode, t0, y0, tEvent + 120, y); Assert.assertEquals(tEvent + 120, finalT, 5.0e-6); for (int i = 0; i < y.length; ++i) { Assert.assertEquals(y0[i] * Math.exp(k[i] * (finalT - t0)), y[i], 1.0e-9); } } public void testSanityChecks() { try { TestProblem1 pb = new TestProblem1(); new ClassicalRungeKuttaIntegrator(0.01).integrate(pb, 0.0, new double[pb.getDimension()+10], 1.0, new double[pb.getDimension()]); fail("an exception should have been thrown"); } catch(DerivativeException de) { fail("wrong exception caught"); } catch(IntegratorException ie) { } try { TestProblem1 pb = new TestProblem1(); new ClassicalRungeKuttaIntegrator(0.01).integrate(pb, 0.0, new double[pb.getDimension()], 1.0, new double[pb.getDimension()+10]); fail("an exception should have been thrown"); } catch(DerivativeException de) { fail("wrong exception caught"); } catch(IntegratorException ie) { } try { TestProblem1 pb = new TestProblem1(); new ClassicalRungeKuttaIntegrator(0.01).integrate(pb, 0.0, new double[pb.getDimension()], 0.0, new double[pb.getDimension()]); fail("an exception should have been thrown"); } catch(DerivativeException de) { fail("wrong exception caught"); } catch(IntegratorException ie) { } } public void testDecreasingSteps() throws DerivativeException, IntegratorException { TestProblemAbstract[] problems = TestProblemFactory.getProblems(); for (int k = 0; k < problems.length; ++k) { double previousError = Double.NaN; for (int i = 4; i < 10; ++i) { TestProblemAbstract pb = problems[k].copy(); double step = (pb.getFinalTime() - pb.getInitialTime()) * Math.pow(2.0, -i); FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step); TestProblemHandler handler = new TestProblemHandler(pb, integ); integ.addStepHandler(handler); EventHandler[] functions = pb.getEventsHandlers(); for (int l = 0; l < functions.length; ++l) { integ.addEventHandler(functions[l], Double.POSITIVE_INFINITY, 1.0e-6 * step, 1000); } assertEquals(functions.length, integ.getEventHandlers().size()); double stopTime = integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[pb.getDimension()]); if (functions.length == 0) { assertEquals(pb.getFinalTime(), stopTime, 1.0e-10); } double error = handler.getMaximalValueError(); if (i > 4) { assertTrue(error < Math.abs(previousError)); } previousError = error; assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); integ.clearEventHandlers(); assertEquals(0, integ.getEventHandlers().size()); } } } public void testSmallStep() throws DerivativeException, IntegratorException { TestProblem1 pb = new TestProblem1(); double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001; FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step); TestProblemHandler handler = new TestProblemHandler(pb, integ); integ.addStepHandler(handler); integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[pb.getDimension()]); assertTrue(handler.getLastError() < 2.0e-13); assertTrue(handler.getMaximalValueError() < 4.0e-12); assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); assertEquals("classical Runge-Kutta", integ.getName()); } public void testBigStep() throws DerivativeException, IntegratorException { TestProblem1 pb = new TestProblem1(); double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2; FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step); TestProblemHandler handler = new TestProblemHandler(pb, integ); integ.addStepHandler(handler); integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[pb.getDimension()]); assertTrue(handler.getLastError() > 0.0004); assertTrue(handler.getMaximalValueError() > 0.005); assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); } public void testBackward() throws DerivativeException, IntegratorException { TestProblem5 pb = new TestProblem5(); double step = Math.abs(pb.getFinalTime() - pb.getInitialTime()) * 0.001; FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step); TestProblemHandler handler = new TestProblemHandler(pb, integ); integ.addStepHandler(handler); integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[pb.getDimension()]); assertTrue(handler.getLastError() < 5.0e-10); assertTrue(handler.getMaximalValueError() < 7.0e-10); assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); assertEquals("classical Runge-Kutta", integ.getName()); } public void testKepler() throws DerivativeException, IntegratorException { final TestProblem3 pb = new TestProblem3(0.9); double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003; FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step); integ.addStepHandler(new KeplerHandler(pb)); integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[pb.getDimension()]); } private static class KeplerHandler implements StepHandler { public KeplerHandler(TestProblem3 pb) { this.pb = pb; reset(); } public boolean requiresDenseOutput() { return false; } public void reset() { maxError = 0; } public void handleStep(StepInterpolator interpolator, boolean isLast) throws DerivativeException { double[] interpolatedY = interpolator.getInterpolatedState (); double[] theoreticalY = pb.computeTheoreticalState(interpolator.getCurrentTime()); double dx = interpolatedY[0] - theoreticalY[0]; double dy = interpolatedY[1] - theoreticalY[1]; double error = dx * dx + dy * dy; if (error > maxError) { maxError = error; } if (isLast) { // even with more than 1000 evaluations per period, // RK4 is not able to integrate such an eccentric // orbit with a good accuracy assertTrue(maxError > 0.005); } } private double maxError = 0; private TestProblem3 pb; } public void testStepSize() throws DerivativeException, IntegratorException { final double step = 1.23456; FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step); integ.addStepHandler(new StepHandler() { public void handleStep(StepInterpolator interpolator, boolean isLast) { if (! isLast) { assertEquals(step, interpolator.getCurrentTime() - interpolator.getPreviousTime(), 1.0e-12); } } public boolean requiresDenseOutput() { return false; } public void reset() { } }); integ.integrate(new FirstOrderDifferentialEquations() { private static final long serialVersionUID = 0L; public void computeDerivatives(double t, double[] y, double[] dot) { dot[0] = 1.0; } public int getDimension() { return 1; } }, 0.0, new double[] { 0.0 }, 5.0, new double[1]); } } Other Commons Math examples (source code examples)Here is a short list of links related to this Commons Math ClassicalRungeKuttaIntegratorTest.java source code file: |
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