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// to you under the Apache License, Version 2.0 (the
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//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing,
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package org.apache.commons.math.optimization.fitting;
import static org.junit.Assert.assertEquals;
import static org.junit.Assert.assertTrue;
import java.util.Random;
import org.apache.commons.math.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math.optimization.DifferentiableMultivariateVectorialOptimizer;
import org.apache.commons.math.optimization.OptimizationException;
import org.apache.commons.math.optimization.general.GaussNewtonOptimizer;
import org.apache.commons.math.optimization.general.LevenbergMarquardtOptimizer;
import org.apache.commons.math.util.FastMath;
import org.junit.Test;
public class PolynomialFitterTest {
@Test
public void testNoError() throws OptimizationException {
Random randomizer = new Random(64925784252l);
for (int degree = 1; degree < 10; ++degree) {
PolynomialFunction p = buildRandomPolynomial(degree, randomizer);
PolynomialFitter fitter =
new PolynomialFitter(degree, new LevenbergMarquardtOptimizer());
for (int i = 0; i <= degree; ++i) {
fitter.addObservedPoint(1.0, i, p.value(i));
}
PolynomialFunction fitted = fitter.fit();
for (double x = -1.0; x < 1.0; x += 0.01) {
double error = FastMath.abs(p.value(x) - fitted.value(x)) /
(1.0 + FastMath.abs(p.value(x)));
assertEquals(0.0, error, 1.0e-6);
}
}
}
@Test
public void testSmallError() throws OptimizationException {
Random randomizer = new Random(53882150042l);
double maxError = 0;
for (int degree = 0; degree < 10; ++degree) {
PolynomialFunction p = buildRandomPolynomial(degree, randomizer);
PolynomialFitter fitter =
new PolynomialFitter(degree, new LevenbergMarquardtOptimizer());
for (double x = -1.0; x < 1.0; x += 0.01) {
fitter.addObservedPoint(1.0, x,
p.value(x) + 0.1 * randomizer.nextGaussian());
}
PolynomialFunction fitted = fitter.fit();
for (double x = -1.0; x < 1.0; x += 0.01) {
double error = FastMath.abs(p.value(x) - fitted.value(x)) /
(1.0 + FastMath.abs(p.value(x)));
maxError = FastMath.max(maxError, error);
assertTrue(FastMath.abs(error) < 0.1);
}
}
assertTrue(maxError > 0.01);
}
@Test
public void testRedundantSolvable() {
// Levenberg-Marquardt should handle redundant information gracefully
checkUnsolvableProblem(new LevenbergMarquardtOptimizer(), true);
}
@Test
public void testRedundantUnsolvable() {
// Gauss-Newton should not be able to solve redundant information
DifferentiableMultivariateVectorialOptimizer optimizer =
new GaussNewtonOptimizer(true);
checkUnsolvableProblem(optimizer, false);
}
private void checkUnsolvableProblem(DifferentiableMultivariateVectorialOptimizer optimizer,
boolean solvable) {
Random randomizer = new Random(1248788532l);
for (int degree = 0; degree < 10; ++degree) {
PolynomialFunction p = buildRandomPolynomial(degree, randomizer);
PolynomialFitter fitter = new PolynomialFitter(degree, optimizer);
// reusing the same point over and over again does not bring
// information, the problem cannot be solved in this case for
// degrees greater than 1 (but one point is sufficient for
// degree 0)
for (double x = -1.0; x < 1.0; x += 0.01) {
fitter.addObservedPoint(1.0, 0.0, p.value(0.0));
}
try {
fitter.fit();
assertTrue(solvable || (degree == 0));
} catch(OptimizationException e) {
assertTrue((! solvable) && (degree > 0));
}
}
}
private PolynomialFunction buildRandomPolynomial(int degree, Random randomizer) {
final double[] coefficients = new double[degree + 1];
for (int i = 0; i <= degree; ++i) {
coefficients[i] = randomizer.nextGaussian();
}
return new PolynomialFunction(coefficients);
}
}