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Commons Math example source code file (NelderMeadTest.java)

This example Commons Math source code file (NelderMeadTest.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Java - Commons Math tags/keywords

array2drowrealmatrix, convergenceexception, convergenceexception, functionevaluationexception, functionevaluationexception, leastsquaresconverter, multivariaterealfunction, neldermead, neldermead, powell, realpointvaluepair, rosenbrock, test, test

The Commons Math NelderMeadTest.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.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.analysis.MultivariateVectorialFunction;
import org.apache.commons.math.linear.Array2DRowRealMatrix;
import org.apache.commons.math.linear.RealMatrix;
import org.apache.commons.math.optimization.GoalType;
import org.apache.commons.math.optimization.LeastSquaresConverter;
import org.apache.commons.math.optimization.OptimizationException;
import org.apache.commons.math.optimization.RealPointValuePair;
import org.apache.commons.math.optimization.SimpleRealPointChecker;
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
  public void testLeastSquares1()
  throws FunctionEvaluationException, ConvergenceException {

      final RealMatrix factors =
          new Array2DRowRealMatrix(new double[][] {
              { 1.0, 0.0 },
              { 0.0, 1.0 }
          }, false);
      LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorialFunction() {
          public double[] value(double[] variables) {
              return factors.operate(variables);
          }
      }, new double[] { 2.0, -3.0 });
      NelderMead optimizer = new NelderMead();
      optimizer.setConvergenceChecker(new SimpleScalarValueChecker(-1.0, 1.0e-6));
      optimizer.setMaxIterations(200);
      RealPointValuePair optimum =
          optimizer.optimize(ls, GoalType.MINIMIZE, new double[] { 10.0, 10.0 });
      assertEquals( 2.0, optimum.getPointRef()[0], 3.0e-5);
      assertEquals(-3.0, optimum.getPointRef()[1], 4.0e-4);
      assertTrue(optimizer.getEvaluations() > 60);
      assertTrue(optimizer.getEvaluations() < 80);
      assertTrue(optimum.getValue() < 1.0e-6);
  }

  @Test
  public void testLeastSquares2()
  throws FunctionEvaluationException, ConvergenceException {

      final RealMatrix factors =
          new Array2DRowRealMatrix(new double[][] {
              { 1.0, 0.0 },
              { 0.0, 1.0 }
          }, false);
      LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorialFunction() {
          public double[] value(double[] variables) {
              return factors.operate(variables);
          }
      }, new double[] { 2.0, -3.0 }, new double[] { 10.0, 0.1 });
      NelderMead optimizer = new NelderMead();
      optimizer.setConvergenceChecker(new SimpleScalarValueChecker(-1.0, 1.0e-6));
      optimizer.setMaxIterations(200);
      RealPointValuePair optimum =
          optimizer.optimize(ls, GoalType.MINIMIZE, new double[] { 10.0, 10.0 });
      assertEquals( 2.0, optimum.getPointRef()[0], 5.0e-5);
      assertEquals(-3.0, optimum.getPointRef()[1], 8.0e-4);
      assertTrue(optimizer.getEvaluations() > 60);
      assertTrue(optimizer.getEvaluations() < 80);
      assertTrue(optimum.getValue() < 1.0e-6);
  }

  @Test
  public void testLeastSquares3()
  throws FunctionEvaluationException, ConvergenceException {

      final RealMatrix factors =
          new Array2DRowRealMatrix(new double[][] {
              { 1.0, 0.0 },
              { 0.0, 1.0 }
          }, false);
      LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorialFunction() {
          public double[] value(double[] variables) {
              return factors.operate(variables);
          }
      }, new double[] { 2.0, -3.0 }, new Array2DRowRealMatrix(new double [][] {
          { 1.0, 1.2 }, { 1.2, 2.0 }
      }));
      NelderMead optimizer = new NelderMead();
      optimizer.setConvergenceChecker(new SimpleScalarValueChecker(-1.0, 1.0e-6));
      optimizer.setMaxIterations(200);
      RealPointValuePair optimum =
          optimizer.optimize(ls, GoalType.MINIMIZE, new double[] { 10.0, 10.0 });
      assertEquals( 2.0, optimum.getPointRef()[0], 2.0e-3);
      assertEquals(-3.0, optimum.getPointRef()[1], 8.0e-4);
      assertTrue(optimizer.getEvaluations() > 60);
      assertTrue(optimizer.getEvaluations() < 80);
      assertTrue(optimum.getValue() < 1.0e-6);
  }

  @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 SimpleRealPointChecker(-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;
      }

  }

}

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