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 * 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
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 * 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
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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() {
	}
	// Defects4J: flaky method
	// 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;
	}

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

}
