| /* |
| * 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.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 GraggBulirschStoerIntegratorTest { |
| |
| @Test(expected=DimensionMismatchException.class) |
| public void testDimensionCheck() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| TestProblem1 pb = new TestProblem1(); |
| AdaptiveStepsizeIntegrator integrator = |
| new GraggBulirschStoerIntegrator(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 testNullIntervalCheck() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| TestProblem1 pb = new TestProblem1(); |
| GraggBulirschStoerIntegrator integrator = |
| new GraggBulirschStoerIntegrator(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()]); |
| } |
| |
| @Test(expected=NumberIsTooSmallException.class) |
| public void testMinStep() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| TestProblem5 pb = new TestProblem5(); |
| double minStep = 0.1 * AccurateMath.abs(pb.getFinalTime() - pb.getInitialTime()); |
| double maxStep = AccurateMath.abs(pb.getFinalTime() - pb.getInitialTime()); |
| double[] vecAbsoluteTolerance = { 1.0e-20, 1.0e-21 }; |
| double[] vecRelativeTolerance = { 1.0e-20, 1.0e-21 }; |
| |
| FirstOrderIntegrator integ = |
| new GraggBulirschStoerIntegrator(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()]); |
| |
| } |
| |
| @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 GraggBulirschStoerIntegrator(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() < 7.5e-9); |
| Assert.assertTrue(handler.getMaximalValueError() < 8.1e-9); |
| Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); |
| Assert.assertEquals("Gragg-Bulirsch-Stoer", integ.getName()); |
| } |
| |
| @Test |
| public void testIncreasingTolerance() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| int previousCalls = Integer.MAX_VALUE; |
| for (int i = -12; i < -4; ++i) { |
| TestProblem1 pb = new TestProblem1(); |
| double minStep = 0; |
| double maxStep = pb.getFinalTime() - pb.getInitialTime(); |
| double absTolerance = AccurateMath.pow(10.0, i); |
| double relTolerance = absTolerance; |
| |
| FirstOrderIntegrator integ = |
| new GraggBulirschStoerIntegrator(minStep, maxStep, |
| absTolerance, relTolerance); |
| TestProblemHandler handler = new TestProblemHandler(pb, integ); |
| integ.addStepHandler(handler); |
| integ.integrate(pb, |
| pb.getInitialTime(), pb.getInitialState(), |
| pb.getFinalTime(), new double[pb.getDimension()]); |
| |
| // the coefficients are only valid for this test |
| // and have been obtained from trial and error |
| // there is no general relation between local and global errors |
| double ratio = handler.getMaximalValueError() / absTolerance; |
| Assert.assertTrue(ratio < 2.4); |
| Assert.assertTrue(ratio > 0.02); |
| 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 testIntegratorControls() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| TestProblem3 pb = new TestProblem3(0.999); |
| GraggBulirschStoerIntegrator integ = |
| new GraggBulirschStoerIntegrator(0, pb.getFinalTime() - pb.getInitialTime(), |
| 1.0e-8, 1.0e-10); |
| |
| double errorWithDefaultSettings = getMaxError(integ, pb); |
| |
| // stability control |
| integ.setStabilityCheck(true, 2, 1, 0.99); |
| Assert.assertTrue(errorWithDefaultSettings < getMaxError(integ, pb)); |
| integ.setStabilityCheck(true, -1, -1, -1); |
| |
| integ.setControlFactors(0.5, 0.99, 0.1, 2.5); |
| Assert.assertTrue(errorWithDefaultSettings < getMaxError(integ, pb)); |
| integ.setControlFactors(-1, -1, -1, -1); |
| |
| integ.setOrderControl(10, 0.7, 0.95); |
| Assert.assertTrue(errorWithDefaultSettings < getMaxError(integ, pb)); |
| integ.setOrderControl(-1, -1, -1); |
| |
| integ.setInterpolationControl(true, 3); |
| Assert.assertTrue(errorWithDefaultSettings < getMaxError(integ, pb)); |
| integ.setInterpolationControl(true, -1); |
| |
| } |
| |
| private double getMaxError(FirstOrderIntegrator integrator, TestProblemAbstract pb) |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| TestProblemHandler handler = new TestProblemHandler(pb, integrator); |
| integrator.addStepHandler(handler); |
| integrator.integrate(pb, |
| pb.getInitialTime(), pb.getInitialState(), |
| pb.getFinalTime(), new double[pb.getDimension()]); |
| return handler.getMaximalValueError(); |
| } |
| |
| @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-10; |
| double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance; |
| |
| FirstOrderIntegrator integ = new GraggBulirschStoerIntegrator(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() < 4.0e-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 absTolerance = 1.0e-6; |
| double relTolerance = 1.0e-6; |
| |
| FirstOrderIntegrator integ = |
| new GraggBulirschStoerIntegrator(minStep, maxStep, |
| absTolerance, relTolerance); |
| integ.addStepHandler(new KeplerStepHandler(pb)); |
| integ.integrate(pb, |
| pb.getInitialTime(), pb.getInitialState(), |
| pb.getFinalTime(), new double[pb.getDimension()]); |
| |
| Assert.assertEquals(integ.getEvaluations(), pb.getCalls()); |
| Assert.assertTrue(pb.getCalls() < 2150); |
| |
| } |
| |
| @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 absTolerance = 1.0e-8; |
| double relTolerance = 1.0e-8; |
| FirstOrderIntegrator integ = |
| new GraggBulirschStoerIntegrator(minStep, maxStep, |
| absTolerance, relTolerance); |
| integ.addStepHandler(new VariableStepHandler()); |
| 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("Gragg-Bulirsch-Stoer", integ.getName()); |
| } |
| |
| @Test |
| public void testTooLargeFirstStep() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| |
| AdaptiveStepsizeIntegrator integ = |
| new GraggBulirschStoerIntegrator(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 >= AccurateMath.nextAfter(start, Double.NEGATIVE_INFINITY)); |
| Assert.assertTrue(t <= AccurateMath.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 testUnstableDerivative() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| final StepProblem stepProblem = new StepProblem(0.0, 1.0, 2.0); |
| FirstOrderIntegrator integ = |
| new GraggBulirschStoerIntegrator(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 testIssue596() |
| throws DimensionMismatchException, NumberIsTooSmallException, |
| MaxCountExceededException, NoBracketingException { |
| FirstOrderIntegrator integ = new GraggBulirschStoerIntegrator(1e-10, 100.0, 1e-7, 1e-7); |
| integ.addStepHandler(new StepHandler() { |
| |
| @Override |
| public void init(double t0, double[] y0, double t) { |
| } |
| |
| @Override |
| public void handleStep(StepInterpolator interpolator, boolean isLast) |
| throws MaxCountExceededException { |
| double t = interpolator.getCurrentTime(); |
| interpolator.setInterpolatedTime(t); |
| double[] y = interpolator.getInterpolatedState(); |
| double[] yDot = interpolator.getInterpolatedDerivatives(); |
| Assert.assertEquals(3.0 * t - 5.0, y[0], 1.0e-14); |
| Assert.assertEquals(3.0, yDot[0], 1.0e-14); |
| } |
| }); |
| double[] y = {4.0}; |
| double t0 = 3.0; |
| double tend = 10.0; |
| integ.integrate(new FirstOrderDifferentialEquations() { |
| @Override |
| public int getDimension() { |
| return 1; |
| } |
| |
| @Override |
| public void computeDerivatives(double t, double[] y, double[] yDot) { |
| yDot[0] = 3.0; |
| } |
| }, t0, y, tend, y); |
| |
| } |
| |
| private static class KeplerStepHandler implements StepHandler { |
| KeplerStepHandler(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 < 100; ++a) { |
| |
| double prev = interpolator.getPreviousTime(); |
| double curr = interpolator.getCurrentTime(); |
| double interp = ((100 - a) * prev + a * curr) / 100; |
| 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 < 2.7e-6); |
| Assert.assertTrue(nbSteps < 80); |
| } |
| } |
| private int nbSteps; |
| private double maxError; |
| private TestProblem3 pb; |
| } |
| |
| public static class VariableStepHandler implements StepHandler { |
| public VariableStepHandler() { |
| 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 < 8.2e-3); |
| Assert.assertTrue(maxStep > 1.5); |
| } |
| } |
| private boolean firstTime; |
| private double minStep; |
| private double maxStep; |
| } |
| |
| } |