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* http://www.apache.org/licenses/LICENSE-2.0
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package org.apache.commons.math4.optim.nonlinear.scalar.noderiv;
import org.apache.commons.math4.analysis.MultivariateFunction;
import org.apache.commons.math4.analysis.MultivariateVectorFunction;
import org.apache.commons.math4.exception.MathUnsupportedOperationException;
import org.apache.commons.math4.exception.TooManyEvaluationsException;
import org.apache.commons.math4.linear.Array2DRowRealMatrix;
import org.apache.commons.math4.linear.RealMatrix;
import org.apache.commons.math4.optim.InitialGuess;
import org.apache.commons.math4.optim.MaxEval;
import org.apache.commons.math4.optim.PointValuePair;
import org.apache.commons.math4.optim.SimpleBounds;
import org.apache.commons.math4.optim.nonlinear.scalar.GoalType;
import org.apache.commons.math4.optim.nonlinear.scalar.LeastSquaresConverter;
import org.apache.commons.math4.optim.nonlinear.scalar.ObjectiveFunction;
import org.apache.commons.math4.optim.nonlinear.scalar.noderiv.NelderMeadSimplex;
import org.apache.commons.math4.optim.nonlinear.scalar.noderiv.SimplexOptimizer;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
public class SimplexOptimizerNelderMeadTest {
@Test(expected=MathUnsupportedOperationException.class)
public void testBoundsUnsupported() {
SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
final FourExtrema fourExtrema = new FourExtrema();
optimizer.optimize(new MaxEval(100),
new ObjectiveFunction(fourExtrema),
GoalType.MINIMIZE,
new InitialGuess(new double[] { -3, 0 }),
new NelderMeadSimplex(new double[] { 0.2, 0.2 }),
new SimpleBounds(new double[] { -5, -1 },
new double[] { 5, 1 }));
}
@Test
public void testMinimize1() {
SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
final FourExtrema fourExtrema = new FourExtrema();
final PointValuePair optimum
= optimizer.optimize(new MaxEval(100),
new ObjectiveFunction(fourExtrema),
GoalType.MINIMIZE,
new InitialGuess(new double[] { -3, 0 }),
new NelderMeadSimplex(new double[] { 0.2, 0.2 }));
Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 2e-7);
Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 2e-5);
Assert.assertEquals(fourExtrema.valueXmYp, optimum.getValue(), 6e-12);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 90);
// Check that the number of iterations is updated (MATH-949).
Assert.assertTrue(optimizer.getIterations() > 0);
}
@Test
public void testMinimize2() {
SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
final FourExtrema fourExtrema = new FourExtrema();
final PointValuePair optimum
= optimizer.optimize(new MaxEval(100),
new ObjectiveFunction(fourExtrema),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 1, 0 }),
new NelderMeadSimplex(new double[] { 0.2, 0.2 }));
Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 5e-6);
Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 6e-6);
Assert.assertEquals(fourExtrema.valueXpYm, optimum.getValue(), 1e-11);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 90);
// Check that the number of iterations is updated (MATH-949).
Assert.assertTrue(optimizer.getIterations() > 0);
}
@Test
public void testMaximize1() {
SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
final FourExtrema fourExtrema = new FourExtrema();
final PointValuePair optimum
= optimizer.optimize(new MaxEval(100),
new ObjectiveFunction(fourExtrema),
GoalType.MAXIMIZE,
new InitialGuess(new double[] { -3, 0 }),
new NelderMeadSimplex(new double[] { 0.2, 0.2 }));
Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 1e-5);
Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 3e-6);
Assert.assertEquals(fourExtrema.valueXmYm, optimum.getValue(), 3e-12);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 90);
// Check that the number of iterations is updated (MATH-949).
Assert.assertTrue(optimizer.getIterations() > 0);
}
@Test
public void testMaximize2() {
SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
final FourExtrema fourExtrema = new FourExtrema();
final PointValuePair optimum
= optimizer.optimize(new MaxEval(100),
new ObjectiveFunction(fourExtrema),
GoalType.MAXIMIZE,
new InitialGuess(new double[] { 1, 0 }),
new NelderMeadSimplex(new double[] { 0.2, 0.2 }));
Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 4e-6);
Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 5e-6);
Assert.assertEquals(fourExtrema.valueXpYp, optimum.getValue(), 7e-12);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 90);
// Check that the number of iterations is updated (MATH-949).
Assert.assertTrue(optimizer.getIterations() > 0);
}
@Test
public void testRosenbrock() {
Rosenbrock rosenbrock = new Rosenbrock();
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3);
PointValuePair optimum
= optimizer.optimize(new MaxEval(100),
new ObjectiveFunction(rosenbrock),
GoalType.MINIMIZE,
new InitialGuess(new double[] { -1.2, 1 }),
new NelderMeadSimplex(new double[][] {
{ -1.2, 1 },
{ 0.9, 1.2 },
{ 3.5, -2.3 } }));
Assert.assertEquals(rosenbrock.getCount(), optimizer.getEvaluations());
Assert.assertTrue(optimizer.getEvaluations() > 40);
Assert.assertTrue(optimizer.getEvaluations() < 50);
Assert.assertTrue(optimum.getValue() < 8e-4);
}
@Test
public void testPowell() {
Powell powell = new Powell();
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3);
PointValuePair optimum =
optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(powell),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 3, -1, 0, 1 }),
new NelderMeadSimplex(4));
Assert.assertEquals(powell.getCount(), optimizer.getEvaluations());
Assert.assertTrue(optimizer.getEvaluations() > 110);
Assert.assertTrue(optimizer.getEvaluations() < 130);
Assert.assertTrue(optimum.getValue() < 2e-3);
}
@Test
public void testLeastSquares1() {
final RealMatrix factors
= new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
@Override
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2.0, -3.0 });
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
PointValuePair optimum =
optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(ls),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 10, 10 }),
new NelderMeadSimplex(2));
Assert.assertEquals( 2, optimum.getPointRef()[0], 3e-5);
Assert.assertEquals(-3, optimum.getPointRef()[1], 4e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1.0e-6);
}
@Test
public void testLeastSquares2() {
final RealMatrix factors
= new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
@Override
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2, -3 }, new double[] { 10, 0.1 });
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
PointValuePair optimum =
optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(ls),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 10, 10 }),
new NelderMeadSimplex(2));
Assert.assertEquals( 2, optimum.getPointRef()[0], 5e-5);
Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1e-6);
}
@Test
public void testLeastSquares3() {
final RealMatrix factors =
new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
@Override
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2, -3 }, new Array2DRowRealMatrix(new double [][] {
{ 1, 1.2 }, { 1.2, 2 }
}));
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
PointValuePair optimum
= optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(ls),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 10, 10 }),
new NelderMeadSimplex(2));
Assert.assertEquals( 2, optimum.getPointRef()[0], 2e-3);
Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1e-6);
}
@Test(expected=TooManyEvaluationsException.class)
public void testMaxIterations() {
Powell powell = new Powell();
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3);
optimizer.optimize(new MaxEval(20),
new ObjectiveFunction(powell),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 3, -1, 0, 1 }),
new NelderMeadSimplex(4));
}
private static class FourExtrema implements MultivariateFunction {
// 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.
@Override
public double value(double[] variables) {
final double x = variables[0];
final double y = variables[1];
return (x == 0 || y == 0) ? 0 :
FastMath.atan(x) * FastMath.atan(x + 2) * FastMath.atan(y) * FastMath.atan(y) / (x * y);
}
}
private static class Rosenbrock implements MultivariateFunction {
private int count;
public Rosenbrock() {
count = 0;
}
@Override
public double value(double[] x) {
++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 MultivariateFunction {
private int count;
public Powell() {
count = 0;
}
@Override
public double value(double[] x) {
++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;
}
}
}