/* * 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 org.apache.commons.math.exception.MathUserException; 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.GillIntegrator; import org.apache.commons.math.ode.sampling.StepHandler; import org.apache.commons.math.ode.sampling.StepInterpolator; import org.apache.commons.math.util.FastMath; import org.junit.Assert; import org.junit.Test; public class GillIntegratorTest { @Test public void testDimensionCheck() { try { TestProblem1 pb = new TestProblem1(); new GillIntegrator(0.01).integrate(pb, 0.0, new double[pb.getDimension()+10], 1.0, new double[pb.getDimension()+10]); Assert.fail("an exception should have been thrown"); } catch(MathUserException de) { Assert.fail("wrong exception caught"); } catch(IntegratorException ie) { } } @Test public void testDecreasingSteps() throws MathUserException, IntegratorException { TestProblemAbstract[] problems = TestProblemFactory.getProblems(); for (int k = 0; k < problems.length; ++k) { double previousValueError = Double.NaN; double previousTimeError = Double.NaN; for (int i = 5; i < 10; ++i) { TestProblemAbstract pb = problems[k].copy(); double step = (pb.getFinalTime() - pb.getInitialTime()) * FastMath.pow(2.0, -i); FirstOrderIntegrator integ = new GillIntegrator(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); } double stopTime = integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[pb.getDimension()]); if (functions.length == 0) { Assert.assertEquals(pb.getFinalTime(), stopTime, 1.0e-10); } double valueError = handler.getMaximalValueError(); if (i > 5) { Assert.assertTrue(valueError < FastMath.abs(previousValueError)); } previousValueError = valueError; double timeError = handler.getMaximalTimeError(); if (i > 5) { Assert.assertTrue(timeError <= FastMath.abs(previousTimeError)); } previousTimeError = timeError; } } } @Test public void testSmallStep() throws MathUserException, IntegratorException { TestProblem1 pb = new TestProblem1(); double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001; FirstOrderIntegrator integ = new GillIntegrator(step); TestProblemHandler handler = new TestProblemHandler(pb, integ); integ.addStepHandler(handler); integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[pb.getDimension()]); Assert.assertTrue(handler.getLastError() < 2.0e-13); Assert.assertTrue(handler.getMaximalValueError() < 4.0e-12); Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); Assert.assertEquals("Gill", integ.getName()); } @Test public void testBigStep() throws MathUserException, IntegratorException { TestProblem1 pb = new TestProblem1(); double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2; FirstOrderIntegrator integ = new GillIntegrator(step); TestProblemHandler handler = new TestProblemHandler(pb, integ); integ.addStepHandler(handler); integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[pb.getDimension()]); Assert.assertTrue(handler.getLastError() > 0.0004); Assert.assertTrue(handler.getMaximalValueError() > 0.005); Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); } @Test public void testBackward() throws MathUserException, IntegratorException { TestProblem5 pb = new TestProblem5(); double step = FastMath.abs(pb.getFinalTime() - pb.getInitialTime()) * 0.001; FirstOrderIntegrator integ = new GillIntegrator(step); TestProblemHandler handler = new TestProblemHandler(pb, integ); integ.addStepHandler(handler); integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[pb.getDimension()]); Assert.assertTrue(handler.getLastError() < 5.0e-10); Assert.assertTrue(handler.getMaximalValueError() < 7.0e-10); Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); Assert.assertEquals("Gill", integ.getName()); } @Test public void testKepler() throws MathUserException, IntegratorException { final TestProblem3 pb = new TestProblem3(0.9); double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003; FirstOrderIntegrator integ = new GillIntegrator(step); integ.addStepHandler(new KeplerStepHandler(pb)); integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[pb.getDimension()]); } @Test public void testUnstableDerivative() throws MathUserException, IntegratorException { final StepProblem stepProblem = new StepProblem(0.0, 1.0, 2.0); FirstOrderIntegrator integ = new GillIntegrator(0.3); integ.addEventHandler(stepProblem, 1.0, 1.0e-12, 1000); double[] y = { Double.NaN }; integ.integrate(stepProblem, 0.0, new double[] { 0.0 }, 10.0, y); Assert.assertEquals(8.0, y[0], 1.0e-12); } private static class KeplerStepHandler implements StepHandler { public KeplerStepHandler(TestProblem3 pb) { this.pb = pb; reset(); } public void reset() { maxError = 0; } public void handleStep(StepInterpolator interpolator, boolean isLast) throws MathUserException { 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 Assert.assertTrue(maxError > 0.001); } } private double maxError; private TestProblem3 pb; } @Test public void testStepSize() throws MathUserException, IntegratorException { final double step = 1.23456; FirstOrderIntegrator integ = new GillIntegrator(step); integ.addStepHandler(new StepHandler() { public void handleStep(StepInterpolator interpolator, boolean isLast) { if (! isLast) { Assert.assertEquals(step, interpolator.getCurrentTime() - interpolator.getPreviousTime(), 1.0e-12); } } public void reset() { } }); integ.integrate(new FirstOrderDifferentialEquations() { 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]); } }