commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/optim/nonlinear/scalar/noderiv/PowellOptimizerTest.java - commons-math - Git at Google

 /*
  * 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.math4.legacy.optim.nonlinear.scalar.noderiv;

 import org.apache.commons.math4.legacy.analysis.MultivariateFunction;
 import org.apache.commons.math4.legacy.analysis.SumSincFunction;
 import org.apache.commons.math4.legacy.exception.MathUnsupportedOperationException;
 import org.apache.commons.math4.legacy.optim.InitialGuess;
 import org.apache.commons.math4.legacy.optim.MaxEval;
 import org.apache.commons.math4.legacy.optim.PointValuePair;
 import org.apache.commons.math4.legacy.optim.SimpleBounds;
 import org.apache.commons.math4.legacy.optim.nonlinear.scalar.GoalType;
 import org.apache.commons.math4.legacy.optim.nonlinear.scalar.ObjectiveFunction;
 import org.apache.commons.math4.core.jdkmath.JdkMath;
 import org.junit.Assert;
 import org.junit.Test;

 /**
  * Test for {@link PowellOptimizer}.
  */
 public class PowellOptimizerTest {
     @Test(expected=MathUnsupportedOperationException.class)
     public void testBoundsUnsupported() {
         final MultivariateFunction func = new SumSincFunction(-1);
         final PowellOptimizer optim = new PowellOptimizer(1e-8, 1e-5,
                                                           1e-4, 1e-4);

         optim.optimize(new MaxEval(100),
                        new ObjectiveFunction(func),
                        GoalType.MINIMIZE,
                        new InitialGuess(new double[] { -3, 0 }),
                        new SimpleBounds(new double[] { -5, -1 },
                                         new double[] { 5, 1 }));
     }

     @Test
     public void testSumSinc() {
         final MultivariateFunction func = new SumSincFunction(-1);

         int dim = 2;
         final double[] minPoint = new double[dim];
         for (int i = 0; i < dim; i++) {
             minPoint[i] = 0;
         }

         double[] init = new double[dim];

         // Initial is minimum.
         for (int i = 0; i < dim; i++) {
             init[i] = minPoint[i];
         }
         doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-9);

         // Initial is far from minimum.
         for (int i = 0; i < dim; i++) {
             init[i] = minPoint[i] + 3;
         }
         doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-5);
         // More stringent line search tolerance enhances the precision
         // of the result.
         doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-9, 1e-7);
     }

     @Test
     public void testQuadratic() {
         final MultivariateFunction func = new MultivariateFunction() {
                 @Override
                 public double value(double[] x) {
                     final double a = x[0] - 1;
                     final double b = x[1] - 1;
                     return a * a + b * b + 1;
                 }
             };

         int dim = 2;
         final double[] minPoint = new double[dim];
         for (int i = 0; i < dim; i++) {
             minPoint[i] = 1;
         }

         double[] init = new double[dim];

         // Initial is minimum.
         for (int i = 0; i < dim; i++) {
             init[i] = minPoint[i];
         }
         doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-8);

         // Initial is far from minimum.
         for (int i = 0; i < dim; i++) {
             init[i] = minPoint[i] - 20;
         }
         doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-8);
     }

     @Test
     public void testMaximizeQuadratic() {
         final MultivariateFunction func = new MultivariateFunction() {
                 @Override
                 public double value(double[] x) {
                     final double a = x[0] - 1;
                     final double b = x[1] - 1;
                     return -a * a - b * b + 1;
                 }
             };

         int dim = 2;
         final double[] maxPoint = new double[dim];
         for (int i = 0; i < dim; i++) {
             maxPoint[i] = 1;
         }

         double[] init = new double[dim];

         // Initial is minimum.
         for (int i = 0; i < dim; i++) {
             init[i] = maxPoint[i];
         }
         doTest(func, maxPoint, init,  GoalType.MAXIMIZE, 1e-9, 1e-8);

         // Initial is far from minimum.
         for (int i = 0; i < dim; i++) {
             init[i] = maxPoint[i] - 20;
         }
         doTest(func, maxPoint, init, GoalType.MAXIMIZE, 1e-9, 1e-8);
     }

     /**
      * Ensure that we do not increase the number of function evaluations when
      * the function values are scaled up.
      * Note that the tolerances parameters passed to the constructor must
      * still hold sensible values because they are used to set the line search
      * tolerances.
      */
     @Test
     public void testRelativeToleranceOnScaledValues() {
         final MultivariateFunction func = new MultivariateFunction() {
                 @Override
                 public double value(double[] x) {
                     final double a = x[0] - 1;
                     final double b = x[1] - 1;
                     return a * a * JdkMath.sqrt(JdkMath.abs(a)) + b * b + 1;
                 }
             };

         int dim = 2;
         final double[] minPoint = new double[dim];
         for (int i = 0; i < dim; i++) {
             minPoint[i] = 1;
         }

         double[] init = new double[dim];
         // Initial is far from minimum.
         for (int i = 0; i < dim; i++) {
             init[i] = minPoint[i] - 20;
         }

         final double relTol = 1e-10;

         final int maxEval = 1000;
         // Very small absolute tolerance to rely solely on the relative
         // tolerance as a stopping criterion
         final PowellOptimizer optim = new PowellOptimizer(relTol, 1e-100);

         final PointValuePair funcResult = optim.optimize(new MaxEval(maxEval),
                                                          new ObjectiveFunction(func),
                                                          GoalType.MINIMIZE,
                                                          new InitialGuess(init));
         final double funcValue = func.value(funcResult.getPoint());
         final int funcEvaluations = optim.getEvaluations();

         final double scale = 1e10;
         final MultivariateFunction funcScaled = new MultivariateFunction() {
                 @Override
                 public double value(double[] x) {
                     return scale * func.value(x);
                 }
             };

         final PointValuePair funcScaledResult = optim.optimize(new MaxEval(maxEval),
                                                                new ObjectiveFunction(funcScaled),
                                                                GoalType.MINIMIZE,
                                                                new InitialGuess(init));
         final double funcScaledValue = funcScaled.value(funcScaledResult.getPoint());
         final int funcScaledEvaluations = optim.getEvaluations();

         // Check that both minima provide the same objective funciton values,
         // within the relative function tolerance.
         Assert.assertEquals(1, funcScaledValue / (scale * funcValue), relTol);

         // Check that the numbers of evaluations are the same.
         Assert.assertEquals(funcEvaluations, funcScaledEvaluations);
     }

     /**
      * @param func Function to optimize.
      * @param optimum Expected optimum.
      * @param init Starting point.
      * @param goal Minimization or maximization.
      * @param fTol Tolerance (relative error on the objective function) for
      * "Powell" algorithm.
      * @param pointTol Tolerance for checking that the optimum is correct.
      */
     private void doTest(MultivariateFunction func,
                         double[] optimum,
                         double[] init,
                         GoalType goal,
                         double fTol,
                         double pointTol) {
         final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d));

         final PointValuePair result = optim.optimize(new MaxEval(1000),
                                                      new ObjectiveFunction(func),
                                                      goal,
                                                      new InitialGuess(init));
         final double[] point = result.getPoint();

         for (int i = 0, dim = optimum.length; i < dim; i++) {
             Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),
                                 optimum[i], point[i], pointTol);
         }
     }

     /**
      * @param func Function to optimize.
      * @param optimum Expected optimum.
      * @param init Starting point.
      * @param goal Minimization or maximization.
      * @param fTol Tolerance (relative error on the objective function) for
      * "Powell" algorithm.
      * @param fLineTol Tolerance (relative error on the objective function)
      * for the internal line search algorithm.
      * @param pointTol Tolerance for checking that the optimum is correct.
      */
     private void doTest(MultivariateFunction func,
                         double[] optimum,
                         double[] init,
                         GoalType goal,
                         double fTol,
                         double fLineTol,
                         double pointTol) {
         final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d),
                                                           fLineTol, Math.ulp(1d));

         final PointValuePair result = optim.optimize(new MaxEval(1000),
                                                      new ObjectiveFunction(func),
                                                      goal,
                                                      new InitialGuess(init));
         final double[] point = result.getPoint();

         for (int i = 0, dim = optimum.length; i < dim; i++) {
             Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),
                                 optimum[i], point[i], pointTol);
         }

         Assert.assertTrue(optim.getIterations() > 0);
     }
 }
	/*
	* 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.math4.legacy.optim.nonlinear.scalar.noderiv;

	import org.apache.commons.math4.legacy.analysis.MultivariateFunction;
	import org.apache.commons.math4.legacy.analysis.SumSincFunction;
	import org.apache.commons.math4.legacy.exception.MathUnsupportedOperationException;
	import org.apache.commons.math4.legacy.optim.InitialGuess;
	import org.apache.commons.math4.legacy.optim.MaxEval;
	import org.apache.commons.math4.legacy.optim.PointValuePair;
	import org.apache.commons.math4.legacy.optim.SimpleBounds;
	import org.apache.commons.math4.legacy.optim.nonlinear.scalar.GoalType;
	import org.apache.commons.math4.legacy.optim.nonlinear.scalar.ObjectiveFunction;
	import org.apache.commons.math4.core.jdkmath.JdkMath;
	import org.junit.Assert;
	import org.junit.Test;

	/**
	* Test for {@link PowellOptimizer}.
	*/
	public class PowellOptimizerTest {
	@Test(expected=MathUnsupportedOperationException.class)
	public void testBoundsUnsupported() {
	final MultivariateFunction func = new SumSincFunction(-1);
	final PowellOptimizer optim = new PowellOptimizer(1e-8, 1e-5,
	1e-4, 1e-4);

	optim.optimize(new MaxEval(100),
	new ObjectiveFunction(func),
	GoalType.MINIMIZE,
	new InitialGuess(new double[] { -3, 0 }),
	new SimpleBounds(new double[] { -5, -1 },
	new double[] { 5, 1 }));
	}

	@Test
	public void testSumSinc() {
	final MultivariateFunction func = new SumSincFunction(-1);

	int dim = 2;
	final double[] minPoint = new double[dim];
	for (int i = 0; i < dim; i++) {
	minPoint[i] = 0;
	}

	double[] init = new double[dim];

	// Initial is minimum.
	for (int i = 0; i < dim; i++) {
	init[i] = minPoint[i];
	}
	doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-9);

	// Initial is far from minimum.
	for (int i = 0; i < dim; i++) {
	init[i] = minPoint[i] + 3;
	}
	doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-5);
	// More stringent line search tolerance enhances the precision
	// of the result.
	doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-9, 1e-7);
	}

	@Test
	public void testQuadratic() {
	final MultivariateFunction func = new MultivariateFunction() {
	@Override
	public double value(double[] x) {
	final double a = x[0] - 1;
	final double b = x[1] - 1;
	return a * a + b * b + 1;
	}
	};

	int dim = 2;
	final double[] minPoint = new double[dim];
	for (int i = 0; i < dim; i++) {
	minPoint[i] = 1;
	}

	double[] init = new double[dim];

	// Initial is minimum.
	for (int i = 0; i < dim; i++) {
	init[i] = minPoint[i];
	}
	doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-8);

	// Initial is far from minimum.
	for (int i = 0; i < dim; i++) {
	init[i] = minPoint[i] - 20;
	}
	doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-8);
	}

	@Test
	public void testMaximizeQuadratic() {
	final MultivariateFunction func = new MultivariateFunction() {
	@Override
	public double value(double[] x) {
	final double a = x[0] - 1;
	final double b = x[1] - 1;
	return -a * a - b * b + 1;
	}
	};

	int dim = 2;
	final double[] maxPoint = new double[dim];
	for (int i = 0; i < dim; i++) {
	maxPoint[i] = 1;
	}

	double[] init = new double[dim];

	// Initial is minimum.
	for (int i = 0; i < dim; i++) {
	init[i] = maxPoint[i];
	}
	doTest(func, maxPoint, init, GoalType.MAXIMIZE, 1e-9, 1e-8);

	// Initial is far from minimum.
	for (int i = 0; i < dim; i++) {
	init[i] = maxPoint[i] - 20;
	}
	doTest(func, maxPoint, init, GoalType.MAXIMIZE, 1e-9, 1e-8);
	}

	/**
	* Ensure that we do not increase the number of function evaluations when
	* the function values are scaled up.
	* Note that the tolerances parameters passed to the constructor must
	* still hold sensible values because they are used to set the line search
	* tolerances.
	*/
	@Test
	public void testRelativeToleranceOnScaledValues() {
	final MultivariateFunction func = new MultivariateFunction() {
	@Override
	public double value(double[] x) {
	final double a = x[0] - 1;
	final double b = x[1] - 1;
	return a * a * JdkMath.sqrt(JdkMath.abs(a)) + b * b + 1;
	}
	};

	int dim = 2;
	final double[] minPoint = new double[dim];
	for (int i = 0; i < dim; i++) {
	minPoint[i] = 1;
	}

	double[] init = new double[dim];
	// Initial is far from minimum.
	for (int i = 0; i < dim; i++) {
	init[i] = minPoint[i] - 20;
	}

	final double relTol = 1e-10;

	final int maxEval = 1000;
	// Very small absolute tolerance to rely solely on the relative
	// tolerance as a stopping criterion
	final PowellOptimizer optim = new PowellOptimizer(relTol, 1e-100);

	final PointValuePair funcResult = optim.optimize(new MaxEval(maxEval),
	new ObjectiveFunction(func),
	GoalType.MINIMIZE,
	new InitialGuess(init));
	final double funcValue = func.value(funcResult.getPoint());
	final int funcEvaluations = optim.getEvaluations();

	final double scale = 1e10;
	final MultivariateFunction funcScaled = new MultivariateFunction() {
	@Override
	public double value(double[] x) {
	return scale * func.value(x);
	}
	};

	final PointValuePair funcScaledResult = optim.optimize(new MaxEval(maxEval),
	new ObjectiveFunction(funcScaled),
	GoalType.MINIMIZE,
	new InitialGuess(init));
	final double funcScaledValue = funcScaled.value(funcScaledResult.getPoint());
	final int funcScaledEvaluations = optim.getEvaluations();

	// Check that both minima provide the same objective funciton values,
	// within the relative function tolerance.
	Assert.assertEquals(1, funcScaledValue / (scale * funcValue), relTol);

	// Check that the numbers of evaluations are the same.
	Assert.assertEquals(funcEvaluations, funcScaledEvaluations);
	}

	/**
	* @param func Function to optimize.
	* @param optimum Expected optimum.
	* @param init Starting point.
	* @param goal Minimization or maximization.
	* @param fTol Tolerance (relative error on the objective function) for
	* "Powell" algorithm.
	* @param pointTol Tolerance for checking that the optimum is correct.
	*/
	private void doTest(MultivariateFunction func,
	double[] optimum,
	double[] init,
	GoalType goal,
	double fTol,
	double pointTol) {
	final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d));

	final PointValuePair result = optim.optimize(new MaxEval(1000),
	new ObjectiveFunction(func),
	goal,
	new InitialGuess(init));
	final double[] point = result.getPoint();

	for (int i = 0, dim = optimum.length; i < dim; i++) {
	Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),
	optimum[i], point[i], pointTol);
	}
	}

	/**
	* @param func Function to optimize.
	* @param optimum Expected optimum.
	* @param init Starting point.
	* @param goal Minimization or maximization.
	* @param fTol Tolerance (relative error on the objective function) for
	* "Powell" algorithm.
	* @param fLineTol Tolerance (relative error on the objective function)
	* for the internal line search algorithm.
	* @param pointTol Tolerance for checking that the optimum is correct.
	*/
	private void doTest(MultivariateFunction func,
	double[] optimum,
	double[] init,
	GoalType goal,
	double fTol,
	double fLineTol,
	double pointTol) {
	final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d),
	fLineTol, Math.ulp(1d));

	final PointValuePair result = optim.optimize(new MaxEval(1000),
	new ObjectiveFunction(func),
	goal,
	new InitialGuess(init));
	final double[] point = result.getPoint();

	for (int i = 0, dim = optimum.length; i < dim; i++) {
	Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),
	optimum[i], point[i], pointTol);
	}

	Assert.assertTrue(optim.getIterations() > 0);
	}
	}