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Commons Math example source code file (DormandPrince54IntegratorTest.java)
The Commons Math DormandPrince54IntegratorTest.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.DormandPrince54Integrator; import org.apache.commons.math.ode.nonstiff.EmbeddedRungeKuttaIntegrator; import org.apache.commons.math.ode.sampling.StepHandler; import org.apache.commons.math.ode.sampling.StepInterpolator; import junit.framework.*; public class DormandPrince54IntegratorTest extends TestCase { public DormandPrince54IntegratorTest(String name) { super(name); } public void testDimensionCheck() { try { 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]); fail("an exception should have been thrown"); } catch(DerivativeException de) { fail("wrong exception caught"); } catch(IntegratorException ie) { } } public void testMinStep() { try { 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()]); fail("an exception should have been thrown"); } catch(DerivativeException de) { fail("wrong exception caught"); } catch(IntegratorException ie) { } } public void testSmallLastStep() throws DerivativeException, IntegratorException { TestProblemAbstract pb = new TestProblem5(); double minStep = 1.25; double maxStep = Math.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()]); assertTrue(handler.wasLastSeen()); assertEquals("Dormand-Prince 5(4)", integ.getName()); } 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 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()]); assertTrue(handler.getLastError() < 2.0e-7); assertTrue(handler.getMaximalValueError() < 2.0e-7); assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); assertEquals("Dormand-Prince 5(4)", integ.getName()); } private static class DP54SmallLastHandler implements StepHandler { public DP54SmallLastHandler(double minStep) { lastSeen = false; this.minStep = minStep; } public boolean requiresDenseOutput() { return false; } public void reset() { } public void handleStep(StepInterpolator interpolator, boolean isLast) { if (isLast) { lastSeen = true; double h = interpolator.getCurrentTime() - interpolator.getPreviousTime(); assertTrue(Math.abs(h) < minStep); } } public boolean wasLastSeen() { return lastSeen; } private boolean lastSeen; private double minStep; } public void testIncreasingTolerance() throws DerivativeException, IntegratorException { 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 = Math.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()]); assertEquals(0.8, integ.getSafety(), 1.0e-12); assertEquals(5.0, integ.getMaxGrowth(), 1.0e-12); 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 assertTrue(handler.getMaximalValueError() < (0.7 * scalAbsoluteTolerance)); assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); int calls = pb.getCalls(); assertEquals(integ.getEvaluations(), calls); assertTrue(calls <= previousCalls); previousCalls = calls; } } public void testEvents() throws DerivativeException, IntegratorException { 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(); 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-6); 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 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()]); assertEquals(integ.getEvaluations(), pb.getCalls()); assertTrue(pb.getCalls() < 2800); } public void testVariableSteps() throws DerivativeException, IntegratorException { 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()]); assertEquals(pb.getFinalTime(), stopTime, 1.0e-10); } private static class KeplerHandler implements StepHandler { public KeplerHandler(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 < 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) { assertTrue(maxError < 7.0e-10); assertTrue(nbSteps < 400); } } private int nbSteps; private double maxError; private TestProblem3 pb; } private static class VariableHandler implements StepHandler { public VariableHandler() { firstTime = true; minStep = 0; maxStep = 0; } 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 < (1.0 / 450.0)); assertTrue(maxStep > (1.0 / 4.2)); } } 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 DormandPrince54IntegratorTest.java source code file: |
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