/*
* 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;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableFunction;
import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
import org.apache.commons.math3.analysis.function.Add;
import org.apache.commons.math3.analysis.function.Constant;
import org.apache.commons.math3.analysis.function.Cos;
import org.apache.commons.math3.analysis.function.Cosh;
import org.apache.commons.math3.analysis.function.Divide;
import org.apache.commons.math3.analysis.function.Identity;
import org.apache.commons.math3.analysis.function.Inverse;
import org.apache.commons.math3.analysis.function.Log;
import org.apache.commons.math3.analysis.function.Max;
import org.apache.commons.math3.analysis.function.Min;
import org.apache.commons.math3.analysis.function.Minus;
import org.apache.commons.math3.analysis.function.Multiply;
import org.apache.commons.math3.analysis.function.Pow;
import org.apache.commons.math3.analysis.function.Power;
import org.apache.commons.math3.analysis.function.Sin;
import org.apache.commons.math3.analysis.function.Sinc;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
/**
* Test for {@link FunctionUtils}.
*/
public class FunctionUtilsTest {
private final double EPS = Math.ulp(1d);
@Test
public void testCompose() {
UnivariateFunction id = new Identity();
Assert.assertEquals(3, FunctionUtils.compose(id, id, id).value(3), EPS);
UnivariateFunction c = new Constant(4);
Assert.assertEquals(4, FunctionUtils.compose(id, c).value(3), EPS);
Assert.assertEquals(4, FunctionUtils.compose(c, id).value(3), EPS);
UnivariateFunction m = new Minus();
Assert.assertEquals(-3, FunctionUtils.compose(m).value(3), EPS);
Assert.assertEquals(3, FunctionUtils.compose(m, m).value(3), EPS);
UnivariateFunction inv = new Inverse();
Assert.assertEquals(-0.25, FunctionUtils.compose(inv, m, c, id).value(3), EPS);
UnivariateFunction pow = new Power(2);
Assert.assertEquals(81, FunctionUtils.compose(pow, pow).value(3), EPS);
}
@Test
public void testComposeDifferentiable() {
UnivariateDifferentiableFunction id = new Identity();
Assert.assertEquals(1, FunctionUtils.compose(id, id, id).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
UnivariateDifferentiableFunction c = new Constant(4);
Assert.assertEquals(0, FunctionUtils.compose(id, c).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
Assert.assertEquals(0, FunctionUtils.compose(c, id).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
UnivariateDifferentiableFunction m = new Minus();
Assert.assertEquals(-1, FunctionUtils.compose(m).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
Assert.assertEquals(1, FunctionUtils.compose(m, m).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
UnivariateDifferentiableFunction inv = new Inverse();
Assert.assertEquals(0.25, FunctionUtils.compose(inv, m, id).value(new DerivativeStructure(1, 1, 0, 2)).getPartialDerivative(1), EPS);
UnivariateDifferentiableFunction pow = new Power(2);
Assert.assertEquals(108, FunctionUtils.compose(pow, pow).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
UnivariateDifferentiableFunction log = new Log();
double a = 9876.54321;
Assert.assertEquals(pow.value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1) / pow.value(a),
FunctionUtils.compose(log, pow).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1), EPS);
}
@Test
public void testAdd() {
UnivariateFunction id = new Identity();
UnivariateFunction c = new Constant(4);
UnivariateFunction m = new Minus();
UnivariateFunction inv = new Inverse();
Assert.assertEquals(4.5, FunctionUtils.add(inv, m, c, id).value(2), EPS);
Assert.assertEquals(4 + 2, FunctionUtils.add(c, id).value(2), EPS);
Assert.assertEquals(4 - 2, FunctionUtils.add(c, FunctionUtils.compose(m, id)).value(2), EPS);
}
@Test
public void testAddDifferentiable() {
UnivariateDifferentiableFunction sin = new Sin();
UnivariateDifferentiableFunction c = new Constant(4);
UnivariateDifferentiableFunction m = new Minus();
UnivariateDifferentiableFunction inv = new Inverse();
final double a = 123.456;
Assert.assertEquals(- 1 / (a * a) -1 + Math.cos(a),
FunctionUtils.add(inv, m, c, sin).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1),
EPS);
}
@Test
public void testMultiply() {
UnivariateFunction c = new Constant(4);
Assert.assertEquals(16, FunctionUtils.multiply(c, c).value(12345), EPS);
UnivariateFunction inv = new Inverse();
UnivariateFunction pow = new Power(2);
Assert.assertEquals(1, FunctionUtils.multiply(FunctionUtils.compose(inv, pow), pow).value(3.5), EPS);
}
@Test
public void testMultiplyDifferentiable() {
UnivariateDifferentiableFunction c = new Constant(4);
UnivariateDifferentiableFunction id = new Identity();
final double a = 1.2345678;
Assert.assertEquals(8 * a, FunctionUtils.multiply(c, id, id).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1), EPS);
UnivariateDifferentiableFunction inv = new Inverse();
UnivariateDifferentiableFunction pow = new Power(2.5);
UnivariateDifferentiableFunction cos = new Cos();
Assert.assertEquals(1.5 * Math.sqrt(a) * Math.cos(a) - Math.pow(a, 1.5) * Math.sin(a),
FunctionUtils.multiply(inv, pow, cos).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1), EPS);
UnivariateDifferentiableFunction cosh = new Cosh();
Assert.assertEquals(1.5 * Math.sqrt(a) * Math.cosh(a) + Math.pow(a, 1.5) * Math.sinh(a),
FunctionUtils.multiply(inv, pow, cosh).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1), 8 * EPS);
}
@Test
public void testCombine() {
BivariateFunction bi = new Add();
UnivariateFunction id = new Identity();
UnivariateFunction m = new Minus();
UnivariateFunction c = FunctionUtils.combine(bi, id, m);
Assert.assertEquals(0, c.value(2.3456), EPS);
bi = new Multiply();
UnivariateFunction inv = new Inverse();
c = FunctionUtils.combine(bi, id, inv);
Assert.assertEquals(1, c.value(2.3456), EPS);
}
@Test
public void testCollector() {
BivariateFunction bi = new Add();
MultivariateFunction coll = FunctionUtils.collector(bi, 0);
Assert.assertEquals(10, coll.value(new double[] {1, 2, 3, 4}), EPS);
bi = new Multiply();
coll = FunctionUtils.collector(bi, 1);
Assert.assertEquals(24, coll.value(new double[] {1, 2, 3, 4}), EPS);
bi = new Max();
coll = FunctionUtils.collector(bi, Double.NEGATIVE_INFINITY);
Assert.assertEquals(10, coll.value(new double[] {1, -2, 7.5, 10, -24, 9.99}), 0);
bi = new Min();
coll = FunctionUtils.collector(bi, Double.POSITIVE_INFINITY);
Assert.assertEquals(-24, coll.value(new double[] {1, -2, 7.5, 10, -24, 9.99}), 0);
}
@Test
public void testSinc() {
BivariateFunction div = new Divide();
UnivariateFunction sin = new Sin();
UnivariateFunction id = new Identity();
UnivariateFunction sinc1 = FunctionUtils.combine(div, sin, id);
UnivariateFunction sinc2 = new Sinc();
for (int i = 0; i < 10; i++) {
double x = Math.random();
Assert.assertEquals(sinc1.value(x), sinc2.value(x), EPS);
}
}
@Test
public void testFixingArguments() {
UnivariateFunction scaler = FunctionUtils.fix1stArgument(new Multiply(), 10);
Assert.assertEquals(1.23456, scaler.value(0.123456), EPS);
UnivariateFunction pow1 = new Power(2);
UnivariateFunction pow2 = FunctionUtils.fix2ndArgument(new Pow(), 2);
for (int i = 0; i < 10; i++) {
double x = Math.random() * 10;
Assert.assertEquals(pow1.value(x), pow2.value(x), 0);
}
}
@Test(expected = NumberIsTooLargeException.class)
public void testSampleWrongBounds(){
FunctionUtils.sample(new Sin(), Math.PI, 0.0, 10);
}
@Test(expected = NotStrictlyPositiveException.class)
public void testSampleNegativeNumberOfPoints(){
FunctionUtils.sample(new Sin(), 0.0, Math.PI, -1);
}
@Test(expected = NotStrictlyPositiveException.class)
public void testSampleNullNumberOfPoints(){
FunctionUtils.sample(new Sin(), 0.0, Math.PI, 0);
}
@Test
public void testSample() {
final int n = 11;
final double min = 0.0;
final double max = Math.PI;
final double[] actual = FunctionUtils.sample(new Sin(), min, max, n);
for (int i = 0; i < n; i++) {
final double x = min + (max - min) / n * i;
Assert.assertEquals("x = " + x, FastMath.sin(x), actual[i], 0.0);
}
}
@Test
@Deprecated
public void testToDifferentiableUnivariateFunction() {
// Sin implements both UnivariateDifferentiableFunction and DifferentiableUnivariateFunction
Sin sin = new Sin();
DifferentiableUnivariateFunction converted = FunctionUtils.toDifferentiableUnivariateFunction(sin);
for (double x = 0.1; x < 0.5; x += 0.01) {
Assert.assertEquals(sin.value(x), converted.value(x), 1.0e-10);
Assert.assertEquals(sin.derivative().value(x), converted.derivative().value(x), 1.0e-10);
}
}
@Test
@Deprecated
public void testToUnivariateDifferential() {
// Sin implements both UnivariateDifferentiableFunction and DifferentiableUnivariateFunction
Sin sin = new Sin();
UnivariateDifferentiableFunction converted = FunctionUtils.toUnivariateDifferential(sin);
for (double x = 0.1; x < 0.5; x += 0.01) {
DerivativeStructure t = new DerivativeStructure(2, 1, x, 1.0, 2.0);
Assert.assertEquals(sin.value(t).getValue(), converted.value(t).getValue(), 1.0e-10);
Assert.assertEquals(sin.value(t).getPartialDerivative(1, 0),
converted.value(t).getPartialDerivative(1, 0),
1.0e-10);
Assert.assertEquals(sin.value(t).getPartialDerivative(0, 1),
converted.value(t).getPartialDerivative(0, 1),
1.0e-10);
}
}
@Test
@Deprecated
public void testToDifferentiableMultivariateFunction() {
MultivariateDifferentiableFunction hypot = new MultivariateDifferentiableFunction() {
public double value(double[] point) {
return FastMath.hypot(point[0], point[1]);
}
public DerivativeStructure value(DerivativeStructure[] point) {
return DerivativeStructure.hypot(point[0], point[1]);
}
};
DifferentiableMultivariateFunction converted = FunctionUtils.toDifferentiableMultivariateFunction(hypot);
for (double x = 0.1; x < 0.5; x += 0.01) {
for (double y = 0.1; y < 0.5; y += 0.01) {
double[] point = new double[] { x, y };
Assert.assertEquals(hypot.value(point), converted.value(point), 1.0e-10);
Assert.assertEquals(x / hypot.value(point), converted.gradient().value(point)[0], 1.0e-10);
Assert.assertEquals(y / hypot.value(point), converted.gradient().value(point)[1], 1.0e-10);
}
}
}
@Test
@Deprecated
public void testToMultivariateDifferentiableFunction() {
DifferentiableMultivariateFunction hypot = new DifferentiableMultivariateFunction() {
public double value(double[] point) {
return FastMath.hypot(point[0], point[1]);
}
public MultivariateFunction partialDerivative(final int k) {
return new MultivariateFunction() {
public double value(double[] point) {
return point[k] / FastMath.hypot(point[0], point[1]);
}
};
}
public MultivariateVectorFunction gradient() {
return new MultivariateVectorFunction() {
public double[] value(double[] point) {
final double h = FastMath.hypot(point[0], point[1]);
return new double[] { point[0] / h, point[1] / h };
}
};
}
};
MultivariateDifferentiableFunction converted = FunctionUtils.toMultivariateDifferentiableFunction(hypot);
for (double x = 0.1; x < 0.5; x += 0.01) {
for (double y = 0.1; y < 0.5; y += 0.01) {
DerivativeStructure[] t = new DerivativeStructure[] {
new DerivativeStructure(3, 1, x, 1.0, 2.0, 3.0 ),
new DerivativeStructure(3, 1, y, 4.0, 5.0, 6.0 )
};
DerivativeStructure h = DerivativeStructure.hypot(t[0], t[1]);
Assert.assertEquals(h.getValue(), converted.value(t).getValue(), 1.0e-10);
Assert.assertEquals(h.getPartialDerivative(1, 0, 0),
converted.value(t).getPartialDerivative(1, 0, 0),
1.0e-10);
Assert.assertEquals(h.getPartialDerivative(0, 1, 0),
converted.value(t).getPartialDerivative(0, 1, 0),
1.0e-10);
Assert.assertEquals(h.getPartialDerivative(0, 0, 1),
converted.value(t).getPartialDerivative(0, 0, 1),
1.0e-10);
}
}
}
}