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Commons Math example source code file (GraggBulirschStoerIntegratorTest.java)
The Commons Math GraggBulirschStoerIntegratorTest.java source code/* * 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.ode.DerivativeException; 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.TestProblem4; import org.apache.commons.math.ode.TestProblem5; import org.apache.commons.math.ode.TestProblemAbstract; import org.apache.commons.math.ode.TestProblemHandler; import org.apache.commons.math.ode.events.EventHandler; import org.apache.commons.math.ode.nonstiff.GraggBulirschStoerIntegrator; import org.apache.commons.math.ode.sampling.StepHandler; import org.apache.commons.math.ode.sampling.StepInterpolator; import junit.framework.*; public class GraggBulirschStoerIntegratorTest extends TestCase { public GraggBulirschStoerIntegratorTest(String name) { super(name); } public void testDimensionCheck() { try { 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]); fail("an exception should have been thrown"); } catch(DerivativeException de) { fail("wrong exception caught"); } catch(IntegratorException ie) { } } public void testNullIntervalCheck() { try { 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()]); fail("an exception should have been thrown"); } catch(DerivativeException de) { fail("wrong exception caught"); } catch(IntegratorException ie) { } } public void testMinStep() { try { TestProblem5 pb = new TestProblem5(); double minStep = 0.1 * Math.abs(pb.getFinalTime() - pb.getInitialTime()); double maxStep = Math.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()]); fail("an exception should have been thrown"); } catch(DerivativeException de) { fail("wrong exception caught"); } catch(IntegratorException ie) { } } public void testBackward() throws DerivativeException, IntegratorException { 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()]); assertTrue(handler.getLastError() < 9.0e-10); assertTrue(handler.getMaximalValueError() < 9.0e-10); assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); assertEquals("Gragg-Bulirsch-Stoer", integ.getName()); } public void testIncreasingTolerance() throws DerivativeException, IntegratorException { 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 = Math.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; assertTrue(ratio < 2.4); assertTrue(ratio > 0.02); assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); int calls = pb.getCalls(); assertEquals(integ.getEvaluations(), calls); assertTrue(calls <= previousCalls); previousCalls = calls; } } public void testIntegratorControls() throws DerivativeException, IntegratorException { 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); assertTrue(errorWithDefaultSettings < getMaxError(integ, pb)); integ.setStabilityCheck(true, -1, -1, -1); integ.setStepsizeControl(0.5, 0.99, 0.1, 2.5); assertTrue(errorWithDefaultSettings < getMaxError(integ, pb)); integ.setStepsizeControl(-1, -1, -1, -1); integ.setOrderControl(10, 0.7, 0.95); assertTrue(errorWithDefaultSettings < getMaxError(integ, pb)); integ.setOrderControl(-1, -1, -1); integ.setInterpolationControl(true, 3); assertTrue(errorWithDefaultSettings < getMaxError(integ, pb)); integ.setInterpolationControl(true, -1); } private double getMaxError(FirstOrderIntegrator integrator, TestProblemAbstract pb) throws DerivativeException, IntegratorException { 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(); } public void testEvents() throws DerivativeException, IntegratorException { 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(); for (int l = 0; l < functions.length; ++l) { integ.addEventHandler(functions[l], Double.POSITIVE_INFINITY, 1.0e-8 * maxStep, 1000); } assertEquals(functions.length, integ.getEventHandlers().size()); integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[pb.getDimension()]); assertTrue(handler.getMaximalValueError() < 5.0e-8); assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); assertEquals(12.0, handler.getLastTime(), 1.0e-8 * maxStep); integ.clearEventHandlers(); assertEquals(0, integ.getEventHandlers().size()); } public void testKepler() throws DerivativeException, IntegratorException { 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()]); assertEquals(integ.getEvaluations(), pb.getCalls()); assertTrue(pb.getCalls() < 2150); } public void testVariableSteps() throws DerivativeException, IntegratorException { 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()]); assertEquals(pb.getFinalTime(), stopTime, 1.0e-10); assertEquals("Gragg-Bulirsch-Stoer", integ.getName()); } public void testUnstableDerivative() throws DerivativeException, IntegratorException { 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); assertEquals(8.0, y[0], 1.0e-12); } private static class KeplerStepHandler implements StepHandler { public KeplerStepHandler(TestProblem3 pb) { this.pb = pb; reset(); } public boolean requiresDenseOutput() { return true; } public void reset() { nbSteps = 0; maxError = 0; } public void handleStep(StepInterpolator interpolator, boolean isLast) throws DerivativeException { ++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) { assertTrue(maxError < 2.7e-6); assertTrue(nbSteps < 80); } } private int nbSteps; private double maxError; private TestProblem3 pb; } public static class VariableStepHandler implements StepHandler { public VariableStepHandler() { reset(); } public boolean requiresDenseOutput() { return false; } public void reset() { firstTime = true; minStep = 0; maxStep = 0; } public void handleStep(StepInterpolator interpolator, boolean isLast) { double step = Math.abs(interpolator.getCurrentTime() - interpolator.getPreviousTime()); if (firstTime) { minStep = Math.abs(step); maxStep = minStep; firstTime = false; } else { if (step < minStep) { minStep = step; } if (step > maxStep) { maxStep = step; } } if (isLast) { assertTrue(minStep < 8.2e-3); assertTrue(maxStep > 1.7); } } private boolean firstTime; private double minStep; private double maxStep; } } Other Commons Math examples (source code examples)Here is a short list of links related to this Commons Math GraggBulirschStoerIntegratorTest.java source code file: |
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