| /* |
| * 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.ode.nonstiff; |
| |
| import org.apache.commons.math4.exception.DimensionMismatchException; |
| import org.apache.commons.math4.exception.MaxCountExceededException; |
| import org.apache.commons.math4.exception.NoBracketingException; |
| import org.apache.commons.math4.exception.NumberIsTooSmallException; |
| import org.apache.commons.math4.ode.FirstOrderDifferentialEquations; |
| import org.apache.commons.math4.ode.FirstOrderIntegrator; |
| import org.apache.commons.math4.ode.TestProblem1; |
| import org.apache.commons.math4.ode.TestProblem3; |
| import org.apache.commons.math4.ode.TestProblem4; |
| import org.apache.commons.math4.ode.TestProblem5; |
| import org.apache.commons.math4.ode.TestProblemHandler; |
| import org.apache.commons.math4.ode.events.EventHandler; |
| import org.apache.commons.math4.ode.sampling.StepHandler; |
| import org.apache.commons.math4.ode.sampling.StepInterpolator; |
| import org.apache.commons.math4.util.FastMath; |
| import org.junit.Assert; |
| import org.junit.Test; |
| |
| |
| public class DormandPrince853IntegratorTest { |
| |
| @Test |
| public void testMissedEndEvent() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| 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() { |
| |
| @Override |
| public int getDimension() { |
| return k.length; |
| } |
| |
| @Override |
| public void computeDerivatives(double t, double[] y, double[] yDot) { |
| for (int i = 0; i < y.length; ++i) { |
| yDot[i] = k[i] * y[i]; |
| } |
| } |
| }; |
| |
| DormandPrince853Integrator integrator = new DormandPrince853Integrator(0.0, 100.0, |
| 1.0e-10, 1.0e-10); |
| |
| double[] y0 = new double[k.length]; |
| for (int i = 0; i < y0.length; ++i) { |
| y0[i] = i + 1; |
| } |
| double[] y = new double[k.length]; |
| |
| integrator.setInitialStepSize(60.0); |
| 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] * FastMath.exp(k[i] * (finalT - t0)), y[i], 1.0e-9); |
| } |
| |
| integrator.setInitialStepSize(60.0); |
| integrator.addEventHandler(new EventHandler() { |
| |
| @Override |
| public void init(double t0, double[] y0, double t) { |
| } |
| |
| @Override |
| public void resetState(double t, double[] y) { |
| } |
| |
| @Override |
| public double g(double t, double[] y) { |
| return t - tEvent; |
| } |
| |
| @Override |
| public Action eventOccurred(double t, double[] y, boolean increasing) { |
| Assert.assertEquals(tEvent, t, 5.0e-6); |
| return Action.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] * FastMath.exp(k[i] * (finalT - t0)), y[i], 1.0e-9); |
| } |
| |
| } |
| |
| @Test(expected=DimensionMismatchException.class) |
| public void testDimensionCheck() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| TestProblem1 pb = new TestProblem1(); |
| DormandPrince853Integrator integrator = new DormandPrince853Integrator(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]); |
| Assert.fail("an exception should have been thrown"); |
| } |
| |
| @Test(expected=NumberIsTooSmallException.class) |
| public void testNullIntervalCheck() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| TestProblem1 pb = new TestProblem1(); |
| DormandPrince853Integrator integrator = new DormandPrince853Integrator(0.0, 1.0, |
| 1.0e-10, 1.0e-10); |
| integrator.integrate(pb, |
| 0.0, new double[pb.getDimension()], |
| 0.0, new double[pb.getDimension()]); |
| Assert.fail("an exception should have been thrown"); |
| } |
| |
| @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 DormandPrince853Integrator(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 testIncreasingTolerance() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| int previousCalls = Integer.MAX_VALUE; |
| AdaptiveStepsizeIntegrator integ = |
| new DormandPrince853Integrator(0, Double.POSITIVE_INFINITY, |
| Double.NaN, Double.NaN); |
| for (int i = -12; i < -2; ++i) { |
| TestProblem1 pb = new TestProblem1(); |
| double minStep = 0; |
| double maxStep = pb.getFinalTime() - pb.getInitialTime(); |
| double scalAbsoluteTolerance = FastMath.pow(10.0, i); |
| double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance; |
| integ.setStepSizeControl(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()]); |
| |
| // the 1.3 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() < (1.3 * 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 testTooLargeFirstStep() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| AdaptiveStepsizeIntegrator integ = |
| new DormandPrince853Integrator(0, Double.POSITIVE_INFINITY, Double.NaN, Double.NaN); |
| final double start = 0.0; |
| final double end = 0.001; |
| FirstOrderDifferentialEquations equations = new FirstOrderDifferentialEquations() { |
| |
| @Override |
| public int getDimension() { |
| return 1; |
| } |
| |
| @Override |
| public void computeDerivatives(double t, double[] y, double[] yDot) { |
| Assert.assertTrue(t >= FastMath.nextAfter(start, Double.NEGATIVE_INFINITY)); |
| Assert.assertTrue(t <= FastMath.nextAfter(end, Double.POSITIVE_INFINITY)); |
| yDot[0] = -100.0 * y[0]; |
| } |
| |
| }; |
| |
| integ.setStepSizeControl(0, 1.0, 1.0e-6, 1.0e-8); |
| integ.integrate(equations, start, new double[] { 1.0 }, end, new double[1]); |
| |
| } |
| |
| @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 DormandPrince853Integrator(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() < 1.1e-7); |
| Assert.assertTrue(handler.getMaximalValueError() < 1.1e-7); |
| Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); |
| Assert.assertEquals("Dormand-Prince 8 (5, 3)", integ.getName()); |
| } |
| |
| @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-9; |
| double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance; |
| |
| FirstOrderIntegrator integ = new DormandPrince853Integrator(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.assertEquals(0, handler.getMaximalValueError(), 2.1e-7); |
| 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 DormandPrince853Integrator(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() < 3300); |
| |
| } |
| |
| @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 DormandPrince853Integrator(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); |
| Assert.assertEquals("Dormand-Prince 8 (5, 3)", integ.getName()); |
| } |
| |
| @Test |
| public void testUnstableDerivative() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| final StepProblem stepProblem = new StepProblem(0.0, 1.0, 2.0); |
| FirstOrderIntegrator integ = |
| new DormandPrince853Integrator(0.1, 10, 1.0e-12, 0.0); |
| 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); |
| } |
| |
| @Test |
| public void testEventsScheduling() { |
| |
| FirstOrderDifferentialEquations sincos = new FirstOrderDifferentialEquations() { |
| |
| @Override |
| public int getDimension() { |
| return 2; |
| } |
| |
| @Override |
| public void computeDerivatives(double t, double[] y, double[] yDot) { |
| yDot[0] = y[1]; |
| yDot[1] = -y[0]; |
| } |
| |
| }; |
| |
| SchedulingChecker sinChecker = new SchedulingChecker(0); // events at 0, PI, 2PI ... |
| SchedulingChecker cosChecker = new SchedulingChecker(1); // events at PI/2, 3PI/2, 5PI/2 ... |
| |
| FirstOrderIntegrator integ = |
| new DormandPrince853Integrator(0.001, 1.0, 1.0e-12, 0.0); |
| integ.addEventHandler(sinChecker, 0.01, 1.0e-7, 100); |
| integ.addStepHandler(sinChecker); |
| integ.addEventHandler(cosChecker, 0.01, 1.0e-7, 100); |
| integ.addStepHandler(cosChecker); |
| double t0 = 0.5; |
| double[] y0 = new double[] { FastMath.sin(t0), FastMath.cos(t0) }; |
| double t = 10.0; |
| double[] y = new double[2]; |
| integ.integrate(sincos, t0, y0, t, y); |
| |
| } |
| |
| private static class SchedulingChecker implements StepHandler, EventHandler { |
| |
| int index; |
| double tMin; |
| |
| public SchedulingChecker(int index) { |
| this.index = index; |
| } |
| |
| @Override |
| public void init(double t0, double[] y0, double t) { |
| tMin = t0; |
| } |
| |
| @Override |
| public void handleStep(StepInterpolator interpolator, boolean isLast) { |
| tMin = interpolator.getCurrentTime(); |
| } |
| |
| @Override |
| public double g(double t, double[] y) { |
| // once a step has been handled by handleStep, |
| // events checking should only refer to dates after the step |
| Assert.assertTrue(t >= tMin); |
| return y[index]; |
| } |
| |
| @Override |
| public Action eventOccurred(double t, double[] y, boolean increasing) { |
| return Action.RESET_STATE; |
| } |
| |
| @Override |
| public void resetState(double t, double[] y) { |
| // in fact, we don't need to reset anything for the test |
| } |
| |
| } |
| |
| private static class KeplerHandler implements StepHandler { |
| public 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 < 2.4e-10); |
| Assert.assertTrue(nbSteps < 150); |
| } |
| } |
| private int nbSteps; |
| private double maxError; |
| private TestProblem3 pb; |
| } |
| |
| private static class VariableHandler implements StepHandler { |
| public 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 = FastMath.abs(interpolator.getCurrentTime() |
| - interpolator.getPreviousTime()); |
| if (firstTime) { |
| minStep = FastMath.abs(step); |
| maxStep = minStep; |
| firstTime = false; |
| } else { |
| if (step < minStep) { |
| minStep = step; |
| } |
| if (step > maxStep) { |
| maxStep = step; |
| } |
| } |
| |
| if (isLast) { |
| Assert.assertTrue(minStep < (1.0 / 100.0)); |
| Assert.assertTrue(maxStep > (1.0 / 2.0)); |
| } |
| } |
| private boolean firstTime = true; |
| private double minStep = 0; |
| private double maxStep = 0; |
| } |
| |
| } |