/*
 * 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.
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package org.apache.commons.math.ode.nonstiff;

import junit.framework.Test;
import junit.framework.TestCase;
import junit.framework.TestSuite;

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.nonstiff.HighamHall54Integrator;
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 < 4e-11);
				assertTrue(nbSteps < 670);
			}
		}

		private TestProblem3 pb;
		private int nbSteps;
		private double maxError;
	}

	public static Test suite() {
		return new TestSuite(HighamHall54IntegratorTest.class);
	}

}
