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Commons Math example source code file (HighamHall54IntegratorTest.java)
The Commons Math HighamHall54IntegratorTest.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 junit.framework.TestCase; import org.apache.commons.math.ConvergenceException; import org.apache.commons.math.ode.DerivativeException; import org.apache.commons.math.ode.FirstOrderDifferentialEquations; 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.TestProblemHandler; import org.apache.commons.math.ode.events.EventException; import org.apache.commons.math.ode.events.EventHandler; import org.apache.commons.math.ode.sampling.StepHandler; import org.apache.commons.math.ode.sampling.StepInterpolator; public class HighamHall54IntegratorTest extends TestCase { public HighamHall54IntegratorTest(String name) { super(name); } public void testWrongDerivative() { try { HighamHall54Integrator integrator = new HighamHall54Integrator(0.0, 1.0, 1.0e-10, 1.0e-10); FirstOrderDifferentialEquations equations = new FirstOrderDifferentialEquations() { private static final long serialVersionUID = -1157081786301178032L; public void computeDerivatives(double t, double[] y, double[] dot) throws DerivativeException { if (t < -0.5) { throw new DerivativeException("{0}", "oops"); } else { throw new DerivativeException(new RuntimeException("oops")); } } public int getDimension() { return 1; } }; try { integrator.integrate(equations, -1.0, new double[1], 0.0, new double[1]); fail("an exception should have been thrown"); } catch(DerivativeException de) { // expected behavior } try { integrator.integrate(equations, 0.0, new double[1], 1.0, new double[1]); fail("an exception should have been thrown"); } catch(DerivativeException de) { // expected behavior } } catch (Exception e) { fail("wrong exception caught: " + e.getMessage()); } } 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 HighamHall54Integrator(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 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; FirstOrderIntegrator integ = new HighamHall54Integrator(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 assertTrue(handler.getMaximalValueError() < (1.3 * scalAbsoluteTolerance)); assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); int calls = pb.getCalls(); assertEquals(integ.getEvaluations(), calls); assertTrue(calls <= previousCalls); previousCalls = calls; } } 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 HighamHall54Integrator(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() < 5.0e-7); assertTrue(handler.getMaximalValueError() < 5.0e-7); assertEquals(0, handler.getMaximalTimeError(), 1.0e-12); assertEquals("Higham-Hall 5(4)", integ.getName()); } 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 HighamHall54Integrator(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() < 1.0e-7); 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 testEventsErrors() { final TestProblem1 pb = new TestProblem1(); double minStep = 0; double maxStep = pb.getFinalTime() - pb.getInitialTime(); double scalAbsoluteTolerance = 1.0e-8; double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance; FirstOrderIntegrator integ = new HighamHall54Integrator(minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance); TestProblemHandler handler = new TestProblemHandler(pb, integ); integ.addStepHandler(handler); integ.addEventHandler(new EventHandler() { public int eventOccurred(double t, double[] y, boolean increasing) { return EventHandler.CONTINUE; } public double g(double t, double[] y) throws EventException { double middle = (pb.getInitialTime() + pb.getFinalTime()) / 2; double offset = t - middle; if (offset > 0) { throw new EventException("Evaluation failed for argument = {0}", t); } return offset; } public void resetState(double t, double[] y) { } private static final long serialVersionUID = 935652725339916361L; }, Double.POSITIVE_INFINITY, 1.0e-8 * maxStep, 1000); try { integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[pb.getDimension()]); fail("an exception should have been thrown"); } catch (IntegratorException ie) { // expected behavior } catch (Exception e) { fail("wrong exception type caught"); } } public void testEventsNoConvergence() { final TestProblem1 pb = new TestProblem1(); double minStep = 0; double maxStep = pb.getFinalTime() - pb.getInitialTime(); double scalAbsoluteTolerance = 1.0e-8; double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance; FirstOrderIntegrator integ = new HighamHall54Integrator(minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance); TestProblemHandler handler = new TestProblemHandler(pb, integ); integ.addStepHandler(handler); integ.addEventHandler(new EventHandler() { public int eventOccurred(double t, double[] y, boolean increasing) { return EventHandler.CONTINUE; } public double g(double t, double[] y) { double middle = (pb.getInitialTime() + pb.getFinalTime()) / 2; double offset = t - middle; return (offset > 0) ? (offset + 0.5) : (offset - 0.5); } public void resetState(double t, double[] y) { } private static final long serialVersionUID = 935652725339916361L; }, Double.POSITIVE_INFINITY, 1.0e-8 * maxStep, 3); try { integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[pb.getDimension()]); fail("an exception should have been thrown"); } catch (IntegratorException ie) { assertTrue(ie.getCause() != null); assertTrue(ie.getCause() instanceof ConvergenceException); } catch (Exception e) { fail("wrong exception type caught"); } } public void testSanityChecks() { try { final TestProblem3 pb = new TestProblem3(0.9); double minStep = 0; double maxStep = pb.getFinalTime() - pb.getInitialTime(); try { FirstOrderIntegrator integ = new HighamHall54Integrator(minStep, maxStep, new double[4], new double[4]); integ.integrate(pb, pb.getInitialTime(), new double[6], pb.getFinalTime(), new double[pb.getDimension()]); fail("an exception should have been thrown"); } catch (IntegratorException ie) { // expected behavior } try { FirstOrderIntegrator integ = new HighamHall54Integrator(minStep, maxStep, new double[4], new double[4]); integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[6]); fail("an exception should have been thrown"); } catch (IntegratorException ie) { // expected behavior } try { FirstOrderIntegrator integ = new HighamHall54Integrator(minStep, maxStep, new double[2], new double[4]); integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[pb.getDimension()]); fail("an exception should have been thrown"); } catch (IntegratorException ie) { // expected behavior } try { FirstOrderIntegrator integ = new HighamHall54Integrator(minStep, maxStep, new double[4], new double[2]); integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[pb.getDimension()]); fail("an exception should have been thrown"); } catch (IntegratorException ie) { // expected behavior } try { FirstOrderIntegrator integ = new HighamHall54Integrator(minStep, maxStep, new double[4], new double[4]); integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getInitialTime(), new double[pb.getDimension()]); fail("an exception should have been thrown"); } catch (IntegratorException ie) { // expected behavior } } catch (Exception e) { fail("wrong exception caught: " + e.getMessage()); } } public void testKepler() throws DerivativeException, IntegratorException { final TestProblem3 pb = new TestProblem3(0.9); double minStep = 0; double maxStep = pb.getFinalTime() - pb.getInitialTime(); double[] vecAbsoluteTolerance = { 1.0e-8, 1.0e-8, 1.0e-10, 1.0e-10 }; double[] vecRelativeTolerance = { 1.0e-10, 1.0e-10, 1.0e-8, 1.0e-8 }; FirstOrderIntegrator integ = new HighamHall54Integrator(minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance); integ.addStepHandler(new KeplerHandler(pb)); integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(), pb.getFinalTime(), new double[pb.getDimension()]); assertEquals("Higham-Hall 5(4)", integ.getName()); } private static class KeplerHandler implements StepHandler { public KeplerHandler(TestProblem3 pb) { this.pb = pb; nbSteps = 0; maxError = 0; } public boolean requiresDenseOutput() { return false; } public void reset() { nbSteps = 0; maxError = 0; } public void handleStep(StepInterpolator interpolator, boolean isLast) throws DerivativeException { ++nbSteps; 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) { assertTrue(maxError < 4.2e-11); assertTrue(nbSteps < 670); } } private TestProblem3 pb; private int nbSteps; private double maxError; } } Other Commons Math examples (source code examples)Here is a short list of links related to this Commons Math HighamHall54IntegratorTest.java source code file: |
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