/*
* 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.math3.analysis.function;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.FunctionUtils;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well1024a;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
/**
* Test for class {@link Logit}.
*/
public class LogitTest {
private final double EPS = Math.ulp(1d);
@Test(expected=OutOfRangeException.class)
public void testPreconditions1() {
final double lo = -1;
final double hi = 2;
final UnivariateFunction f = new Logit(lo, hi);
f.value(lo - 1);
}
@Test(expected=OutOfRangeException.class)
public void testPreconditions2() {
final double lo = -1;
final double hi = 2;
final UnivariateFunction f = new Logit(lo, hi);
f.value(hi + 1);
}
@Test
public void testSomeValues() {
final double lo = 1;
final double hi = 2;
final UnivariateFunction f = new Logit(lo, hi);
Assert.assertEquals(Double.NEGATIVE_INFINITY, f.value(1), EPS);
Assert.assertEquals(Double.POSITIVE_INFINITY, f.value(2), EPS);
Assert.assertEquals(0, f.value(1.5), EPS);
}
@Test
public void testDerivative() {
final double lo = 1;
final double hi = 2;
final Logit f = new Logit(lo, hi);
final DerivativeStructure f15 = f.value(new DerivativeStructure(1, 1, 0, 1.5));
Assert.assertEquals(4, f15.getPartialDerivative(1), EPS);
}
@Test
public void testDerivativeLargeArguments() {
final Logit f = new Logit(1, 2);
for (double arg : new double[] {
Double.NEGATIVE_INFINITY, -Double.MAX_VALUE, -1e155, 1e155, Double.MAX_VALUE, Double.POSITIVE_INFINITY
}) {
try {
f.value(new DerivativeStructure(1, 1, 0, arg));
Assert.fail("an exception should have been thrown");
} catch (OutOfRangeException ore) {
// expected
} catch (Exception e) {
Assert.fail("wrong exception caught: " + e.getMessage());
}
}
}
@Test
public void testDerivativesHighOrder() {
DerivativeStructure l = new Logit(1, 3).value(new DerivativeStructure(1, 5, 0, 1.2));
Assert.assertEquals(-2.1972245773362193828, l.getPartialDerivative(0), 1.0e-16);
Assert.assertEquals(5.5555555555555555555, l.getPartialDerivative(1), 9.0e-16);
Assert.assertEquals(-24.691358024691358025, l.getPartialDerivative(2), 2.0e-14);
Assert.assertEquals(250.34293552812071331, l.getPartialDerivative(3), 2.0e-13);
Assert.assertEquals(-3749.4284407864654778, l.getPartialDerivative(4), 4.0e-12);
Assert.assertEquals(75001.270131585632282, l.getPartialDerivative(5), 8.0e-11);
}
@Test(expected=NullArgumentException.class)
public void testParametricUsage1() {
final Logit.Parametric g = new Logit.Parametric();
g.value(0, null);
}
@Test(expected=DimensionMismatchException.class)
public void testParametricUsage2() {
final Logit.Parametric g = new Logit.Parametric();
g.value(0, new double[] {0});
}
@Test(expected=NullArgumentException.class)
public void testParametricUsage3() {
final Logit.Parametric g = new Logit.Parametric();
g.gradient(0, null);
}
@Test(expected=DimensionMismatchException.class)
public void testParametricUsage4() {
final Logit.Parametric g = new Logit.Parametric();
g.gradient(0, new double[] {0});
}
@Test(expected=OutOfRangeException.class)
public void testParametricUsage5() {
final Logit.Parametric g = new Logit.Parametric();
g.value(-1, new double[] {0, 1});
}
@Test(expected=OutOfRangeException.class)
public void testParametricUsage6() {
final Logit.Parametric g = new Logit.Parametric();
g.value(2, new double[] {0, 1});
}
@Test
public void testParametricValue() {
final double lo = 2;
final double hi = 3;
final Logit f = new Logit(lo, hi);
final Logit.Parametric g = new Logit.Parametric();
Assert.assertEquals(f.value(2), g.value(2, new double[] {lo, hi}), 0);
Assert.assertEquals(f.value(2.34567), g.value(2.34567, new double[] {lo, hi}), 0);
Assert.assertEquals(f.value(3), g.value(3, new double[] {lo, hi}), 0);
}
@Test
public void testValueWithInverseFunction() {
final double lo = 2;
final double hi = 3;
final Logit f = new Logit(lo, hi);
final Sigmoid g = new Sigmoid(lo, hi);
RandomGenerator random = new Well1024a(0x49914cdd9f0b8db5l);
final UnivariateDifferentiableFunction id = FunctionUtils.compose((UnivariateDifferentiableFunction) g,
(UnivariateDifferentiableFunction) f);
for (int i = 0; i < 10; i++) {
final double x = lo + random.nextDouble() * (hi - lo);
Assert.assertEquals(x, id.value(new DerivativeStructure(1, 1, 0, x)).getValue(), EPS);
}
Assert.assertEquals(lo, id.value(new DerivativeStructure(1, 1, 0, lo)).getValue(), EPS);
Assert.assertEquals(hi, id.value(new DerivativeStructure(1, 1, 0, hi)).getValue(), EPS);
}
@Test
public void testDerivativesWithInverseFunction() {
double[] epsilon = new double[] { 1.0e-20, 4.0e-16, 3.0e-15, 2.0e-11, 3.0e-9, 1.0e-6 };
final double lo = 2;
final double hi = 3;
final Logit f = new Logit(lo, hi);
final Sigmoid g = new Sigmoid(lo, hi);
RandomGenerator random = new Well1024a(0x96885e9c1f81cea5l);
final UnivariateDifferentiableFunction id =
FunctionUtils.compose((UnivariateDifferentiableFunction) g, (UnivariateDifferentiableFunction) f);
for (int maxOrder = 0; maxOrder < 6; ++maxOrder) {
double max = 0;
for (int i = 0; i < 10; i++) {
final double x = lo + random.nextDouble() * (hi - lo);
final DerivativeStructure dsX = new DerivativeStructure(1, maxOrder, 0, x);
max = FastMath.max(max, FastMath.abs(dsX.getPartialDerivative(maxOrder) -
id.value(dsX).getPartialDerivative(maxOrder)));
Assert.assertEquals(dsX.getPartialDerivative(maxOrder),
id.value(dsX).getPartialDerivative(maxOrder),
epsilon[maxOrder]);
}
// each function evaluates correctly near boundaries,
// but combination leads to NaN as some intermediate point is infinite
final DerivativeStructure dsLo = new DerivativeStructure(1, maxOrder, 0, lo);
if (maxOrder == 0) {
Assert.assertTrue(Double.isInfinite(f.value(dsLo).getPartialDerivative(maxOrder)));
Assert.assertEquals(lo, id.value(dsLo).getPartialDerivative(maxOrder), epsilon[maxOrder]);
} else if (maxOrder == 1) {
Assert.assertTrue(Double.isInfinite(f.value(dsLo).getPartialDerivative(maxOrder)));
Assert.assertTrue(Double.isNaN(id.value(dsLo).getPartialDerivative(maxOrder)));
} else {
Assert.assertTrue(Double.isNaN(f.value(dsLo).getPartialDerivative(maxOrder)));
Assert.assertTrue(Double.isNaN(id.value(dsLo).getPartialDerivative(maxOrder)));
}
final DerivativeStructure dsHi = new DerivativeStructure(1, maxOrder, 0, hi);
if (maxOrder == 0) {
Assert.assertTrue(Double.isInfinite(f.value(dsHi).getPartialDerivative(maxOrder)));
Assert.assertEquals(hi, id.value(dsHi).getPartialDerivative(maxOrder), epsilon[maxOrder]);
} else if (maxOrder == 1) {
Assert.assertTrue(Double.isInfinite(f.value(dsHi).getPartialDerivative(maxOrder)));
Assert.assertTrue(Double.isNaN(id.value(dsHi).getPartialDerivative(maxOrder)));
} else {
Assert.assertTrue(Double.isNaN(f.value(dsHi).getPartialDerivative(maxOrder)));
Assert.assertTrue(Double.isNaN(id.value(dsHi).getPartialDerivative(maxOrder)));
}
}
}
}