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Java example source code file (FunctionUtilsTest.java)

This example Java source code file (FunctionUtilsTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

constant, deprecated, derivativestructure, differentiablemultivariatefunction, eps, identity, inverse, minus, multivariatedifferentiablefunction, power, sin, test, univariatedifferentiablefunction, univariatefunction

The FunctionUtilsTest.java Java example source code

/*
 * 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 = FastMath.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 + FastMath.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 * FastMath.sqrt(a) * FastMath.cos(a) - FastMath.pow(a, 1.5) * FastMath.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 * FastMath.sqrt(a) * FastMath.cosh(a) + FastMath.pow(a, 1.5) * FastMath.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 = FastMath.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 = FastMath.random() * 10;
            Assert.assertEquals(pow1.value(x), pow2.value(x), 0);
        }
    }

    @Test(expected = NumberIsTooLargeException.class)
    public void testSampleWrongBounds(){
        FunctionUtils.sample(new Sin(), FastMath.PI, 0.0, 10);
    }

    @Test(expected = NotStrictlyPositiveException.class)
    public void testSampleNegativeNumberOfPoints(){
        FunctionUtils.sample(new Sin(), 0.0, FastMath.PI, -1);
    }

    @Test(expected = NotStrictlyPositiveException.class)
    public void testSampleNullNumberOfPoints(){
        FunctionUtils.sample(new Sin(), 0.0, FastMath.PI, 0);
    }

    @Test
    public void testSample() {
        final int n = 11;
        final double min = 0.0;
        final double max = FastMath.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);
            }
        }
    }

}

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