/*
* 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.analysis.function;
import org.apache.commons.math4.analysis.UnivariateFunction;
import org.apache.commons.math4.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math4.analysis.differentiation.UnivariateDifferentiableFunction;
import org.apache.commons.math4.analysis.function.Gaussian;
import org.apache.commons.math4.exception.DimensionMismatchException;
import org.apache.commons.math4.exception.NotStrictlyPositiveException;
import org.apache.commons.math4.exception.NullArgumentException;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
/**
* Test for class {@link Gaussian}.
*/
public class GaussianTest {
private final double EPS = Math.ulp(1d);
@Test(expected=NotStrictlyPositiveException.class)
public void testPreconditions() {
new Gaussian(1, 2, -1);
}
@Test
public void testSomeValues() {
final UnivariateFunction f = new Gaussian();
Assert.assertEquals(1 / FastMath.sqrt(2 * Math.PI), f.value(0), EPS);
}
@Test
public void testLargeArguments() {
final UnivariateFunction f = new Gaussian();
Assert.assertEquals(0, f.value(Double.NEGATIVE_INFINITY), 0);
Assert.assertEquals(0, f.value(-Double.MAX_VALUE), 0);
Assert.assertEquals(0, f.value(-1e2), 0);
Assert.assertEquals(0, f.value(1e2), 0);
Assert.assertEquals(0, f.value(Double.MAX_VALUE), 0);
Assert.assertEquals(0, f.value(Double.POSITIVE_INFINITY), 0);
}
@Test
public void testDerivatives() {
final UnivariateDifferentiableFunction gaussian = new Gaussian(2.0, 0.9, 3.0);
final DerivativeStructure dsX = new DerivativeStructure(1, 4, 0, 1.1);
final DerivativeStructure dsY = gaussian.value(dsX);
Assert.assertEquals( 1.9955604901712128349, dsY.getValue(), EPS);
Assert.assertEquals(-0.044345788670471396332, dsY.getPartialDerivative(1), EPS);
Assert.assertEquals(-0.22074348138190206174, dsY.getPartialDerivative(2), EPS);
Assert.assertEquals( 0.014760030401924800557, dsY.getPartialDerivative(3), EPS);
Assert.assertEquals( 0.073253159785035691678, dsY.getPartialDerivative(4), EPS);
}
@Test
public void testDerivativeLargeArguments() {
final Gaussian f = new Gaussian(0, 1e-50);
Assert.assertEquals(0, f.value(new DerivativeStructure(1, 1, 0, Double.NEGATIVE_INFINITY)).getPartialDerivative(1), 0);
Assert.assertEquals(0, f.value(new DerivativeStructure(1, 1, 0, -Double.MAX_VALUE)).getPartialDerivative(1), 0);
Assert.assertEquals(0, f.value(new DerivativeStructure(1, 1, 0, -1e50)).getPartialDerivative(1), 0);
Assert.assertEquals(0, f.value(new DerivativeStructure(1, 1, 0, -1e2)).getPartialDerivative(1), 0);
Assert.assertEquals(0, f.value(new DerivativeStructure(1, 1, 0, 1e2)).getPartialDerivative(1), 0);
Assert.assertEquals(0, f.value(new DerivativeStructure(1, 1, 0, 1e50)).getPartialDerivative(1), 0);
Assert.assertEquals(0, f.value(new DerivativeStructure(1, 1, 0, Double.MAX_VALUE)).getPartialDerivative(1), 0);
Assert.assertEquals(0, f.value(new DerivativeStructure(1, 1, 0, Double.POSITIVE_INFINITY)).getPartialDerivative(1), 0);
}
@Test
public void testDerivativesNaN() {
final Gaussian f = new Gaussian(0, 1e-50);
final DerivativeStructure fx = f.value(new DerivativeStructure(1, 5, 0, Double.NaN));
for (int i = 0; i <= fx.getOrder(); ++i) {
Assert.assertTrue(Double.isNaN(fx.getPartialDerivative(i)));
}
}
@Test(expected=NullArgumentException.class)
public void testParametricUsage1() {
final Gaussian.Parametric g = new Gaussian.Parametric();
g.value(0, null);
}
@Test(expected=DimensionMismatchException.class)
public void testParametricUsage2() {
final Gaussian.Parametric g = new Gaussian.Parametric();
g.value(0, new double[] {0});
}
@Test(expected=NotStrictlyPositiveException.class)
public void testParametricUsage3() {
final Gaussian.Parametric g = new Gaussian.Parametric();
g.value(0, new double[] {0, 1, 0});
}
@Test(expected=NullArgumentException.class)
public void testParametricUsage4() {
final Gaussian.Parametric g = new Gaussian.Parametric();
g.gradient(0, null);
}
@Test(expected=DimensionMismatchException.class)
public void testParametricUsage5() {
final Gaussian.Parametric g = new Gaussian.Parametric();
g.gradient(0, new double[] {0});
}
@Test(expected=NotStrictlyPositiveException.class)
public void testParametricUsage6() {
final Gaussian.Parametric g = new Gaussian.Parametric();
g.gradient(0, new double[] {0, 1, 0});
}
@Test
public void testParametricValue() {
final double norm = 2;
final double mean = 3;
final double sigma = 4;
final Gaussian f = new Gaussian(norm, mean, sigma);
final Gaussian.Parametric g = new Gaussian.Parametric();
Assert.assertEquals(f.value(-1), g.value(-1, new double[] {norm, mean, sigma}), 0);
Assert.assertEquals(f.value(0), g.value(0, new double[] {norm, mean, sigma}), 0);
Assert.assertEquals(f.value(2), g.value(2, new double[] {norm, mean, sigma}), 0);
}
@Test
public void testParametricGradient() {
final double norm = 2;
final double mean = 3;
final double sigma = 4;
final Gaussian.Parametric f = new Gaussian.Parametric();
final double x = 1;
final double[] grad = f.gradient(1, new double[] {norm, mean, sigma});
final double diff = x - mean;
final double n = FastMath.exp(-diff * diff / (2 * sigma * sigma));
Assert.assertEquals(n, grad[0], EPS);
final double m = norm * n * diff / (sigma * sigma);
Assert.assertEquals(m, grad[1], EPS);
final double s = m * diff / sigma;
Assert.assertEquals(s, grad[2], EPS);
}
}