/*
 * 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.optimization.direct;

import static org.junit.Assert.assertEquals;
import static org.junit.Assert.assertNotNull;
import static org.junit.Assert.assertNull;
import static org.junit.Assert.assertTrue;
import static org.junit.Assert.fail;

import org.apache.commons.math.ConvergenceException;
import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.MathException;
import org.apache.commons.math.MaxEvaluationsExceededException;
import org.apache.commons.math.MaxIterationsExceededException;
import org.apache.commons.math.analysis.MultivariateRealFunction;
import org.apache.commons.math.optimization.GoalType;
import org.apache.commons.math.optimization.OptimizationException;
import org.apache.commons.math.optimization.RealPointValuePair;
import org.apache.commons.math.optimization.SimpleScalarValueChecker;
import org.junit.Test;

public class NelderMeadTest {

	@Test
	public void testFunctionEvaluationExceptions() {
		MultivariateRealFunction wrong = new MultivariateRealFunction() {
			private static final long serialVersionUID = 4751314470965489371L;

			public double value(double[] x) throws FunctionEvaluationException {
				if (x[0] < 0) {
					throw new FunctionEvaluationException(x, "{0}", "oops");
				} else if (x[0] > 1) {
					throw new FunctionEvaluationException(new RuntimeException("oops"), x);
				} else {
					return x[0] * (1 - x[0]);
				}
			}
		};
		try {
			NelderMead optimizer = new NelderMead(0.9, 1.9, 0.4, 0.6);
			optimizer.optimize(wrong, GoalType.MINIMIZE, new double[] { -1.0 });
			fail("an exception should have been thrown");
		} catch (FunctionEvaluationException ce) {
			// expected behavior
			assertNull(ce.getCause());
		} catch (Exception e) {
			fail("wrong exception caught: " + e.getMessage());
		}
		try {
			NelderMead optimizer = new NelderMead(0.9, 1.9, 0.4, 0.6);
			optimizer.optimize(wrong, GoalType.MINIMIZE, new double[] { +2.0 });
			fail("an exception should have been thrown");
		} catch (FunctionEvaluationException ce) {
			// expected behavior
			assertNotNull(ce.getCause());
		} catch (Exception e) {
			fail("wrong exception caught: " + e.getMessage());
		}
	}

	@Test
	public void testMinimizeMaximize() throws FunctionEvaluationException, ConvergenceException {

		// the following function has 4 local extrema:
		final double xM = -3.841947088256863675365;
		final double yM = -1.391745200270734924416;
		final double xP = 0.2286682237349059125691;
		final double yP = -yM;
		final double valueXmYm = 0.2373295333134216789769; // local maximum
		final double valueXmYp = -valueXmYm; // local minimum
		final double valueXpYm = -0.7290400707055187115322; // global minimum
		final double valueXpYp = -valueXpYm; // global maximum
		MultivariateRealFunction fourExtrema = new MultivariateRealFunction() {
			private static final long serialVersionUID = -7039124064449091152L;

			public double value(double[] variables) throws FunctionEvaluationException {
				final double x = variables[0];
				final double y = variables[1];
				return ((x == 0) || (y == 0)) ? 0
						: (Math.atan(x) * Math.atan(x + 2) * Math.atan(y) * Math.atan(y) / (x * y));
			}
		};

		NelderMead optimizer = new NelderMead();
		optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-10, 1.0e-30));
		optimizer.setMaxIterations(100);
		optimizer.setStartConfiguration(new double[] { 0.2, 0.2 });
		RealPointValuePair optimum;

		// minimization
		optimum = optimizer.optimize(fourExtrema, GoalType.MINIMIZE, new double[] { -3.0, 0 });
		assertEquals(xM, optimum.getPoint()[0], 2.0e-7);
		assertEquals(yP, optimum.getPoint()[1], 2.0e-5);
		assertEquals(valueXmYp, optimum.getValue(), 6.0e-12);
		assertTrue(optimizer.getEvaluations() > 60);
		assertTrue(optimizer.getEvaluations() < 90);

		optimum = optimizer.optimize(fourExtrema, GoalType.MINIMIZE, new double[] { +1, 0 });
		assertEquals(xP, optimum.getPoint()[0], 5.0e-6);
		assertEquals(yM, optimum.getPoint()[1], 6.0e-6);
		assertEquals(valueXpYm, optimum.getValue(), 1.0e-11);
		assertTrue(optimizer.getEvaluations() > 60);
		assertTrue(optimizer.getEvaluations() < 90);

		// maximization
		optimum = optimizer.optimize(fourExtrema, GoalType.MAXIMIZE, new double[] { -3.0, 0.0 });
		assertEquals(xM, optimum.getPoint()[0], 1.0e-5);
		assertEquals(yM, optimum.getPoint()[1], 3.0e-6);
		assertEquals(valueXmYm, optimum.getValue(), 3.0e-12);
		assertTrue(optimizer.getEvaluations() > 60);
		assertTrue(optimizer.getEvaluations() < 90);

		optimum = optimizer.optimize(fourExtrema, GoalType.MAXIMIZE, new double[] { +1, 0 });
		assertEquals(xP, optimum.getPoint()[0], 4.0e-6);
		assertEquals(yP, optimum.getPoint()[1], 5.0e-6);
		assertEquals(valueXpYp, optimum.getValue(), 7.0e-12);
		assertTrue(optimizer.getEvaluations() > 60);
		assertTrue(optimizer.getEvaluations() < 90);

	}

	@Test
	public void testRosenbrock() throws FunctionEvaluationException, ConvergenceException {

		Rosenbrock rosenbrock = new Rosenbrock();
		NelderMead optimizer = new NelderMead();
		optimizer.setConvergenceChecker(new SimpleScalarValueChecker(-1, 1.0e-3));
		optimizer.setMaxIterations(100);
		optimizer.setStartConfiguration(new double[][] { { -1.2, 1.0 }, { 0.9, 1.2 }, { 3.5, -2.3 } });
		RealPointValuePair optimum = optimizer.optimize(rosenbrock, GoalType.MINIMIZE, new double[] { -1.2, 1.0 });

		assertEquals(rosenbrock.getCount(), optimizer.getEvaluations());
		assertTrue(optimizer.getEvaluations() > 40);
		assertTrue(optimizer.getEvaluations() < 50);
		assertTrue(optimum.getValue() < 8.0e-4);

	}

	@Test
	public void testPowell() throws FunctionEvaluationException, ConvergenceException {

		Powell powell = new Powell();
		NelderMead optimizer = new NelderMead();
		optimizer.setConvergenceChecker(new SimpleScalarValueChecker(-1.0, 1.0e-3));
		optimizer.setMaxIterations(200);
		RealPointValuePair optimum = optimizer.optimize(powell, GoalType.MINIMIZE,
				new double[] { 3.0, -1.0, 0.0, 1.0 });
		assertEquals(powell.getCount(), optimizer.getEvaluations());
		assertTrue(optimizer.getEvaluations() > 110);
		assertTrue(optimizer.getEvaluations() < 130);
		assertTrue(optimum.getValue() < 2.0e-3);

	}

	@Test(expected = MaxIterationsExceededException.class)
	public void testMaxIterations() throws MathException {
		try {
			Powell powell = new Powell();
			NelderMead optimizer = new NelderMead();
			optimizer.setConvergenceChecker(new SimpleScalarValueChecker(-1.0, 1.0e-3));
			optimizer.setMaxIterations(20);
			optimizer.optimize(powell, GoalType.MINIMIZE, new double[] { 3.0, -1.0, 0.0, 1.0 });
		} catch (OptimizationException oe) {
			if (oe.getCause() instanceof ConvergenceException) {
				throw (ConvergenceException) oe.getCause();
			}
			throw oe;
		}
	}

	@Test(expected = MaxEvaluationsExceededException.class)
	public void testMaxEvaluations() throws MathException {
		try {
			Powell powell = new Powell();
			NelderMead optimizer = new NelderMead();
			optimizer.setConvergenceChecker(new SimpleScalarValueChecker(-1.0, 1.0e-3));
			optimizer.setMaxEvaluations(20);
			optimizer.optimize(powell, GoalType.MINIMIZE, new double[] { 3.0, -1.0, 0.0, 1.0 });
		} catch (FunctionEvaluationException fee) {
			if (fee.getCause() instanceof ConvergenceException) {
				throw (ConvergenceException) fee.getCause();
			}
			throw fee;
		}
	}

	private static class Rosenbrock implements MultivariateRealFunction {

		private int count;

		public Rosenbrock() {
			count = 0;
		}

		public double value(double[] x) throws FunctionEvaluationException {
			++count;
			double a = x[1] - x[0] * x[0];
			double b = 1.0 - x[0];
			return 100 * a * a + b * b;
		}

		public int getCount() {
			return count;
		}

	}

	private static class Powell implements MultivariateRealFunction {

		private int count;

		public Powell() {
			count = 0;
		}

		public double value(double[] x) throws FunctionEvaluationException {
			++count;
			double a = x[0] + 10 * x[1];
			double b = x[2] - x[3];
			double c = x[1] - 2 * x[2];
			double d = x[0] - x[3];
			return a * a + 5 * b * b + c * c * c * c + 10 * d * d * d * d;
		}

		public int getCount() {
			return count;
		}

	}

}
