| /* |
| * 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.math4.legacy.ode.nonstiff; |
| |
| import org.apache.commons.math4.legacy.exception.DimensionMismatchException; |
| import org.apache.commons.math4.legacy.exception.MaxCountExceededException; |
| import org.apache.commons.math4.legacy.exception.NoBracketingException; |
| import org.apache.commons.math4.legacy.exception.NumberIsTooSmallException; |
| import org.apache.commons.math4.legacy.ode.FirstOrderIntegrator; |
| import org.apache.commons.math4.legacy.ode.TestProblem1; |
| import org.apache.commons.math4.legacy.ode.TestProblem3; |
| import org.apache.commons.math4.legacy.ode.TestProblem4; |
| import org.apache.commons.math4.legacy.ode.TestProblem5; |
| import org.apache.commons.math4.legacy.ode.TestProblemAbstract; |
| import org.apache.commons.math4.legacy.ode.TestProblemHandler; |
| import org.apache.commons.math4.legacy.ode.events.EventHandler; |
| import org.apache.commons.math4.legacy.ode.sampling.StepHandler; |
| import org.apache.commons.math4.legacy.ode.sampling.StepInterpolator; |
| import org.apache.commons.math4.legacy.core.jdkmath.AccurateMath; |
| import org.junit.Assert; |
| import org.junit.Test; |
| |
| |
| public class DormandPrince54IntegratorTest { |
| |
| @Test(expected=DimensionMismatchException.class) |
| public void testDimensionCheck() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| TestProblem1 pb = new TestProblem1(); |
| DormandPrince54Integrator integrator = new DormandPrince54Integrator(0.0, 1.0, |
| 1.0e-10, 1.0e-10); |
| integrator.integrate(pb, |
| 0.0, new double[pb.getDimension()+10], |
| 1.0, new double[pb.getDimension()+10]); |
| } |
| |
| @Test(expected=NumberIsTooSmallException.class) |
| public void testMinStep() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| TestProblem1 pb = new TestProblem1(); |
| double minStep = 0.1 * (pb.getFinalTime() - pb.getInitialTime()); |
| double maxStep = pb.getFinalTime() - pb.getInitialTime(); |
| double[] vecAbsoluteTolerance = { 1.0e-15, 1.0e-16 }; |
| double[] vecRelativeTolerance = { 1.0e-15, 1.0e-16 }; |
| |
| FirstOrderIntegrator integ = new DormandPrince54Integrator(minStep, maxStep, |
| vecAbsoluteTolerance, |
| vecRelativeTolerance); |
| TestProblemHandler handler = new TestProblemHandler(pb, integ); |
| integ.addStepHandler(handler); |
| integ.integrate(pb, |
| pb.getInitialTime(), pb.getInitialState(), |
| pb.getFinalTime(), new double[pb.getDimension()]); |
| Assert.fail("an exception should have been thrown"); |
| |
| } |
| |
| @Test |
| public void testSmallLastStep() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| TestProblemAbstract pb = new TestProblem5(); |
| double minStep = 1.25; |
| double maxStep = AccurateMath.abs(pb.getFinalTime() - pb.getInitialTime()); |
| double scalAbsoluteTolerance = 6.0e-4; |
| double scalRelativeTolerance = 6.0e-4; |
| |
| AdaptiveStepsizeIntegrator integ = |
| new DormandPrince54Integrator(minStep, maxStep, |
| scalAbsoluteTolerance, |
| scalRelativeTolerance); |
| |
| DP54SmallLastHandler handler = new DP54SmallLastHandler(minStep); |
| integ.addStepHandler(handler); |
| integ.setInitialStepSize(1.7); |
| integ.integrate(pb, |
| pb.getInitialTime(), pb.getInitialState(), |
| pb.getFinalTime(), new double[pb.getDimension()]); |
| Assert.assertTrue(handler.wasLastSeen()); |
| Assert.assertEquals("Dormand-Prince 5(4)", integ.getName()); |
| |
| } |
| |
| @Test |
| public void testBackward() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| TestProblem5 pb = new TestProblem5(); |
| double minStep = 0; |
| double maxStep = pb.getFinalTime() - pb.getInitialTime(); |
| double scalAbsoluteTolerance = 1.0e-8; |
| double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance; |
| |
| FirstOrderIntegrator integ = new DormandPrince54Integrator(minStep, maxStep, |
| scalAbsoluteTolerance, |
| scalRelativeTolerance); |
| 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-7); |
| Assert.assertTrue(handler.getMaximalValueError() < 2.0e-7); |
| Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); |
| Assert.assertEquals("Dormand-Prince 5(4)", integ.getName()); |
| } |
| |
| private static class DP54SmallLastHandler implements StepHandler { |
| |
| DP54SmallLastHandler(double minStep) { |
| lastSeen = false; |
| this.minStep = minStep; |
| } |
| |
| @Override |
| public void init(double t0, double[] y0, double t) { |
| } |
| |
| @Override |
| public void handleStep(StepInterpolator interpolator, boolean isLast) { |
| if (isLast) { |
| lastSeen = true; |
| double h = interpolator.getCurrentTime() - interpolator.getPreviousTime(); |
| Assert.assertTrue(AccurateMath.abs(h) < minStep); |
| } |
| } |
| |
| public boolean wasLastSeen() { |
| return lastSeen; |
| } |
| |
| private boolean lastSeen; |
| private double minStep; |
| |
| } |
| |
| @Test |
| public void testIncreasingTolerance() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| int previousCalls = Integer.MAX_VALUE; |
| for (int i = -12; i < -2; ++i) { |
| TestProblem1 pb = new TestProblem1(); |
| double minStep = 0; |
| double maxStep = pb.getFinalTime() - pb.getInitialTime(); |
| double scalAbsoluteTolerance = AccurateMath.pow(10.0, i); |
| double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance; |
| |
| EmbeddedRungeKuttaIntegrator integ = |
| new DormandPrince54Integrator(minStep, maxStep, |
| scalAbsoluteTolerance, scalRelativeTolerance); |
| TestProblemHandler handler = new TestProblemHandler(pb, integ); |
| integ.setSafety(0.8); |
| integ.setMaxGrowth(5.0); |
| integ.setMinReduction(0.3); |
| integ.addStepHandler(handler); |
| integ.integrate(pb, |
| pb.getInitialTime(), pb.getInitialState(), |
| pb.getFinalTime(), new double[pb.getDimension()]); |
| Assert.assertEquals(0.8, integ.getSafety(), 1.0e-12); |
| Assert.assertEquals(5.0, integ.getMaxGrowth(), 1.0e-12); |
| Assert.assertEquals(0.3, integ.getMinReduction(), 1.0e-12); |
| |
| // the 0.7 factor is only valid for this test |
| // and has been obtained from trial and error |
| // there is no general relation between local and global errors |
| Assert.assertTrue(handler.getMaximalValueError() < (0.7 * scalAbsoluteTolerance)); |
| Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); |
| |
| int calls = pb.getCalls(); |
| Assert.assertEquals(integ.getEvaluations(), calls); |
| Assert.assertTrue(calls <= previousCalls); |
| previousCalls = calls; |
| |
| } |
| |
| } |
| |
| @Test |
| public void testEvents() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| TestProblem4 pb = new TestProblem4(); |
| double minStep = 0; |
| double maxStep = pb.getFinalTime() - pb.getInitialTime(); |
| double scalAbsoluteTolerance = 1.0e-8; |
| double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance; |
| |
| FirstOrderIntegrator integ = new DormandPrince54Integrator(minStep, maxStep, |
| scalAbsoluteTolerance, |
| scalRelativeTolerance); |
| TestProblemHandler handler = new TestProblemHandler(pb, integ); |
| integ.addStepHandler(handler); |
| EventHandler[] functions = pb.getEventsHandlers(); |
| double convergence = 1.0e-8 * maxStep; |
| for (int l = 0; l < functions.length; ++l) { |
| integ.addEventHandler(functions[l], |
| Double.POSITIVE_INFINITY, convergence, 1000); |
| } |
| Assert.assertEquals(functions.length, integ.getEventHandlers().size()); |
| integ.integrate(pb, |
| pb.getInitialTime(), pb.getInitialState(), |
| pb.getFinalTime(), new double[pb.getDimension()]); |
| |
| Assert.assertTrue(handler.getMaximalValueError() < 5.0e-6); |
| Assert.assertEquals(0, handler.getMaximalTimeError(), convergence); |
| Assert.assertEquals(12.0, handler.getLastTime(), convergence); |
| integ.clearEventHandlers(); |
| Assert.assertEquals(0, integ.getEventHandlers().size()); |
| |
| } |
| |
| @Test |
| public void testKepler() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| final TestProblem3 pb = new TestProblem3(0.9); |
| double minStep = 0; |
| double maxStep = pb.getFinalTime() - pb.getInitialTime(); |
| double scalAbsoluteTolerance = 1.0e-8; |
| double scalRelativeTolerance = scalAbsoluteTolerance; |
| |
| FirstOrderIntegrator integ = new DormandPrince54Integrator(minStep, maxStep, |
| scalAbsoluteTolerance, |
| scalRelativeTolerance); |
| integ.addStepHandler(new KeplerHandler(pb)); |
| integ.integrate(pb, |
| pb.getInitialTime(), pb.getInitialState(), |
| pb.getFinalTime(), new double[pb.getDimension()]); |
| |
| Assert.assertEquals(integ.getEvaluations(), pb.getCalls()); |
| Assert.assertTrue(pb.getCalls() < 2800); |
| |
| } |
| |
| @Test |
| public void testVariableSteps() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| final TestProblem3 pb = new TestProblem3(0.9); |
| double minStep = 0; |
| double maxStep = pb.getFinalTime() - pb.getInitialTime(); |
| double scalAbsoluteTolerance = 1.0e-8; |
| double scalRelativeTolerance = scalAbsoluteTolerance; |
| |
| FirstOrderIntegrator integ = new DormandPrince54Integrator(minStep, maxStep, |
| scalAbsoluteTolerance, |
| scalRelativeTolerance); |
| integ.addStepHandler(new VariableHandler()); |
| double stopTime = integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), |
| pb.getFinalTime(), new double[pb.getDimension()]); |
| Assert.assertEquals(pb.getFinalTime(), stopTime, 1.0e-10); |
| } |
| |
| private static class KeplerHandler implements StepHandler { |
| KeplerHandler(TestProblem3 pb) { |
| this.pb = pb; |
| } |
| @Override |
| public void init(double t0, double[] y0, double t) { |
| nbSteps = 0; |
| maxError = 0; |
| } |
| @Override |
| public void handleStep(StepInterpolator interpolator, boolean isLast) |
| throws MaxCountExceededException { |
| |
| ++nbSteps; |
| for (int a = 1; a < 10; ++a) { |
| |
| double prev = interpolator.getPreviousTime(); |
| double curr = interpolator.getCurrentTime(); |
| double interp = ((10 - a) * prev + a * curr) / 10; |
| interpolator.setInterpolatedTime(interp); |
| |
| double[] interpolatedY = interpolator.getInterpolatedState (); |
| double[] theoreticalY = pb.computeTheoreticalState(interpolator.getInterpolatedTime()); |
| 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) { |
| Assert.assertTrue(maxError < 7.0e-10); |
| Assert.assertTrue(nbSteps < 400); |
| } |
| } |
| private int nbSteps; |
| private double maxError; |
| private TestProblem3 pb; |
| } |
| |
| private static class VariableHandler implements StepHandler { |
| VariableHandler() { |
| firstTime = true; |
| minStep = 0; |
| maxStep = 0; |
| } |
| @Override |
| public void init(double t0, double[] y0, double t) { |
| firstTime = true; |
| minStep = 0; |
| maxStep = 0; |
| } |
| @Override |
| public void handleStep(StepInterpolator interpolator, |
| boolean isLast) { |
| |
| double step = AccurateMath.abs(interpolator.getCurrentTime() |
| - interpolator.getPreviousTime()); |
| if (firstTime) { |
| minStep = AccurateMath.abs(step); |
| maxStep = minStep; |
| firstTime = false; |
| } else { |
| if (step < minStep) { |
| minStep = step; |
| } |
| if (step > maxStep) { |
| maxStep = step; |
| } |
| } |
| |
| if (isLast) { |
| Assert.assertTrue(minStep < (1.0 / 450.0)); |
| Assert.assertTrue(maxStep > (1.0 / 4.2)); |
| } |
| } |
| private boolean firstTime; |
| private double minStep; |
| private double maxStep; |
| } |
| |
| } |