| /* |
| * 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.FirstOrderDifferentialEquations; |
| import org.apache.commons.math4.legacy.ode.FirstOrderIntegrator; |
| import org.apache.commons.math4.legacy.ode.TestProblem1; |
| import org.apache.commons.math4.legacy.ode.TestProblem2; |
| 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.TestProblem6; |
| 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.core.jdkmath.JdkMath; |
| import org.junit.Assert; |
| import org.junit.Test; |
| |
| public class LutherIntegratorTest { |
| |
| @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]; |
| } |
| } |
| }; |
| |
| LutherIntegrator integrator = new LutherIntegrator(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, 1.0e-15); |
| for (int i = 0; i < y.length; ++i) { |
| Assert.assertEquals(y0[i] * JdkMath.exp(k[i] * (finalT - t0)), y[i], 1.0e-15); |
| } |
| |
| 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, 1.0e-15); |
| return Action.CONTINUE; |
| } |
| }, Double.POSITIVE_INFINITY, 1.0e-20, 100); |
| finalT = integrator.integrate(ode, t0, y0, tEvent + 120, y); |
| Assert.assertEquals(tEvent + 120, finalT, 1.0e-15); |
| for (int i = 0; i < y.length; ++i) { |
| Assert.assertEquals(y0[i] * JdkMath.exp(k[i] * (finalT - t0)), y[i], 1.0e-15); |
| } |
| |
| } |
| |
| @Test |
| public void testSanityChecks() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| try { |
| TestProblem1 pb = new TestProblem1(); |
| new LutherIntegrator(0.01).integrate(pb, |
| 0.0, new double[pb.getDimension()+10], |
| 1.0, new double[pb.getDimension()]); |
| Assert.fail("an exception should have been thrown"); |
| } catch(DimensionMismatchException ie) { |
| } |
| try { |
| TestProblem1 pb = new TestProblem1(); |
| new LutherIntegrator(0.01).integrate(pb, |
| 0.0, new double[pb.getDimension()], |
| 1.0, new double[pb.getDimension()+10]); |
| Assert.fail("an exception should have been thrown"); |
| } catch(DimensionMismatchException ie) { |
| } |
| try { |
| TestProblem1 pb = new TestProblem1(); |
| new LutherIntegrator(0.01).integrate(pb, |
| 0.0, new double[pb.getDimension()], |
| 0.0, new double[pb.getDimension()]); |
| Assert.fail("an exception should have been thrown"); |
| } catch(NumberIsTooSmallException ie) { |
| } |
| } |
| |
| @Test |
| public void testDecreasingSteps() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| for (TestProblemAbstract pb : new TestProblemAbstract[] { |
| new TestProblem1(), new TestProblem2(), new TestProblem3(), |
| new TestProblem4(), new TestProblem5(), new TestProblem6() |
| }) { |
| |
| double previousValueError = Double.NaN; |
| double previousTimeError = Double.NaN; |
| for (int i = 4; i < 10; ++i) { |
| |
| double step = (pb.getFinalTime() - pb.getInitialTime()) * JdkMath.pow(2.0, -i); |
| |
| FirstOrderIntegrator integ = new LutherIntegrator(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); |
| } |
| Assert.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) { |
| Assert.assertEquals(pb.getFinalTime(), stopTime, 1.0e-10); |
| } |
| |
| double error = handler.getMaximalValueError(); |
| if (i > 4) { |
| Assert.assertTrue(error < 1.01 * JdkMath.abs(previousValueError)); |
| } |
| previousValueError = error; |
| |
| double timeError = handler.getMaximalTimeError(); |
| if (i > 4) { |
| Assert.assertTrue(timeError <= JdkMath.abs(previousTimeError)); |
| } |
| previousTimeError = timeError; |
| |
| integ.clearEventHandlers(); |
| Assert.assertEquals(0, integ.getEventHandlers().size()); |
| } |
| |
| } |
| |
| } |
| |
| @Test |
| public void testSmallStep() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| TestProblem1 pb = new TestProblem1(); |
| double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001; |
| |
| FirstOrderIntegrator integ = new LutherIntegrator(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() < 9.0e-17); |
| Assert.assertTrue(handler.getMaximalValueError() < 4.0e-15); |
| Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); |
| Assert.assertEquals("Luther", integ.getName()); |
| } |
| |
| @Test |
| public void testBigStep() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| TestProblem1 pb = new TestProblem1(); |
| double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2; |
| |
| FirstOrderIntegrator integ = new LutherIntegrator(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() > 0.00002); |
| Assert.assertTrue(handler.getMaximalValueError() > 0.001); |
| Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); |
| |
| } |
| |
| @Test |
| public void testBackward() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| TestProblem5 pb = new TestProblem5(); |
| double step = JdkMath.abs(pb.getFinalTime() - pb.getInitialTime()) * 0.001; |
| |
| FirstOrderIntegrator integ = new LutherIntegrator(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() < 3.0e-13); |
| Assert.assertTrue(handler.getMaximalValueError() < 5.0e-13); |
| Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); |
| Assert.assertEquals("Luther", integ.getName()); |
| } |
| |
| @Test |
| public void testKepler() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| final TestProblem3 pb = new TestProblem3(0.9); |
| double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003; |
| |
| FirstOrderIntegrator integ = new LutherIntegrator(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 { |
| KeplerHandler(TestProblem3 pb) { |
| this.pb = pb; |
| maxError = 0; |
| } |
| @Override |
| public void init(double t0, double[] y0, double t) { |
| maxError = 0; |
| } |
| @Override |
| public void handleStep(StepInterpolator interpolator, boolean isLast) { |
| |
| 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) { |
| Assert.assertTrue(maxError < 2.2e-7); |
| } |
| } |
| private double maxError = 0; |
| private TestProblem3 pb; |
| } |
| |
| @Test |
| public void testStepSize() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| final double step = 1.23456; |
| FirstOrderIntegrator integ = new LutherIntegrator(step); |
| integ.addStepHandler(new StepHandler() { |
| @Override |
| public void handleStep(StepInterpolator interpolator, boolean isLast) { |
| if (! isLast) { |
| Assert.assertEquals(step, |
| interpolator.getCurrentTime() - interpolator.getPreviousTime(), |
| 1.0e-12); |
| } |
| } |
| @Override |
| public void init(double t0, double[] y0, double t) { |
| } |
| }); |
| integ.integrate(new FirstOrderDifferentialEquations() { |
| @Override |
| public void computeDerivatives(double t, double[] y, double[] dot) { |
| dot[0] = 1.0; |
| } |
| @Override |
| public int getDimension() { |
| return 1; |
| } |
| }, 0.0, new double[] { 0.0 }, 5.0, new double[1]); |
| } |
| |
| @Test |
| public void testSingleStep() { |
| |
| final TestProblem3 pb = new TestProblem3(0.9); |
| double h = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003; |
| |
| RungeKuttaIntegrator integ = new LutherIntegrator(Double.NaN); |
| double t = pb.getInitialTime(); |
| double[] y = pb.getInitialState(); |
| for (int i = 0; i < 100; ++i) { |
| y = integ.singleStep(pb, t, y, t + h); |
| t += h; |
| } |
| double[] yth = pb.computeTheoreticalState(t); |
| double dx = y[0] - yth[0]; |
| double dy = y[1] - yth[1]; |
| double error = dx * dx + dy * dy; |
| Assert.assertEquals(0.0, error, 1.0e-11); |
| } |
| |
| } |
