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Java example source code file (PolynomialFunctionTest.java)

This example Java source code file (PolynomialFunctionTest.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

polynomialfunction, polynomialfunctiontest, string, test

The PolynomialFunctionTest.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.polynomials;

import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.util.FastMath;

import org.junit.Test;
import org.junit.Assert;

/**
 * Tests the PolynomialFunction implementation of a UnivariateFunction.
 *
 */
public final class PolynomialFunctionTest {
    /** Error tolerance for tests */
    protected double tolerance = 1e-12;

    /**
     * tests the value of a constant polynomial.
     *
     * <p>value of this is 2.5 everywhere.

*/ @Test public void testConstants() { double[] c = { 2.5 }; PolynomialFunction f = new PolynomialFunction(c); // verify that we are equal to c[0] at several (nonsymmetric) places Assert.assertEquals(f.value(0), c[0], tolerance); Assert.assertEquals(f.value(-1), c[0], tolerance); Assert.assertEquals(f.value(-123.5), c[0], tolerance); Assert.assertEquals(f.value(3), c[0], tolerance); Assert.assertEquals(f.value(456.89), c[0], tolerance); Assert.assertEquals(f.degree(), 0); Assert.assertEquals(f.derivative().value(0), 0, tolerance); Assert.assertEquals(f.polynomialDerivative().derivative().value(0), 0, tolerance); } /** * tests the value of a linear polynomial. * * <p>This will test the function f(x) = 3*x - 1.5

* <p>This will have the values * <tt>f(0) = -1.5, f(-1) = -4.5, f(-2.5) = -9, * f(0.5) = 0, f(1.5) = 3</tt> and {@code f(3) = 7.5} * </p> */ @Test public void testLinear() { double[] c = { -1.5, 3 }; PolynomialFunction f = new PolynomialFunction(c); // verify that we are equal to c[0] when x=0 Assert.assertEquals(f.value(0), c[0], tolerance); // now check a few other places Assert.assertEquals(-4.5, f.value(-1), tolerance); Assert.assertEquals(-9, f.value(-2.5), tolerance); Assert.assertEquals(0, f.value(0.5), tolerance); Assert.assertEquals(3, f.value(1.5), tolerance); Assert.assertEquals(7.5, f.value(3), tolerance); Assert.assertEquals(f.degree(), 1); Assert.assertEquals(f.polynomialDerivative().derivative().value(0), 0, tolerance); } /** * Tests a second order polynomial. * <p> This will test the function f(x) = 2x^2 - 3x -2 = (2x+1)(x-2)

*/ @Test public void testQuadratic() { double[] c = { -2, -3, 2 }; PolynomialFunction f = new PolynomialFunction(c); // verify that we are equal to c[0] when x=0 Assert.assertEquals(f.value(0), c[0], tolerance); // now check a few other places Assert.assertEquals(0, f.value(-0.5), tolerance); Assert.assertEquals(0, f.value(2), tolerance); Assert.assertEquals(-2, f.value(1.5), tolerance); Assert.assertEquals(7, f.value(-1.5), tolerance); Assert.assertEquals(265.5312, f.value(12.34), tolerance); } /** * This will test the quintic function * f(x) = x^2(x-5)(x+3)(x-1) = x^5 - 3x^4 -13x^3 + 15x^2</p> */ @Test public void testQuintic() { double[] c = { 0, 0, 15, -13, -3, 1 }; PolynomialFunction f = new PolynomialFunction(c); // verify that we are equal to c[0] when x=0 Assert.assertEquals(f.value(0), c[0], tolerance); // now check a few other places Assert.assertEquals(0, f.value(5), tolerance); Assert.assertEquals(0, f.value(1), tolerance); Assert.assertEquals(0, f.value(-3), tolerance); Assert.assertEquals(54.84375, f.value(-1.5), tolerance); Assert.assertEquals(-8.06637, f.value(1.3), tolerance); Assert.assertEquals(f.degree(), 5); } /** * tests the firstDerivative function by comparison * * <p>This will test the functions * {@code f(x) = x^3 - 2x^2 + 6x + 3, g(x) = 3x^2 - 4x + 6} * and {@code h(x) = 6x - 4} */ @Test public void testfirstDerivativeComparison() { double[] f_coeff = { 3, 6, -2, 1 }; double[] g_coeff = { 6, -4, 3 }; double[] h_coeff = { -4, 6 }; PolynomialFunction f = new PolynomialFunction(f_coeff); PolynomialFunction g = new PolynomialFunction(g_coeff); PolynomialFunction h = new PolynomialFunction(h_coeff); // compare f' = g Assert.assertEquals(f.derivative().value(0), g.value(0), tolerance); Assert.assertEquals(f.derivative().value(1), g.value(1), tolerance); Assert.assertEquals(f.derivative().value(100), g.value(100), tolerance); Assert.assertEquals(f.derivative().value(4.1), g.value(4.1), tolerance); Assert.assertEquals(f.derivative().value(-3.25), g.value(-3.25), tolerance); // compare g' = h Assert.assertEquals(g.derivative().value(FastMath.PI), h.value(FastMath.PI), tolerance); Assert.assertEquals(g.derivative().value(FastMath.E), h.value(FastMath.E), tolerance); } @Test public void testString() { PolynomialFunction p = new PolynomialFunction(new double[] { -5, 3, 1 }); checkPolynomial(p, "-5 + 3 x + x^2"); checkPolynomial(new PolynomialFunction(new double[] { 0, -2, 3 }), "-2 x + 3 x^2"); checkPolynomial(new PolynomialFunction(new double[] { 1, -2, 3 }), "1 - 2 x + 3 x^2"); checkPolynomial(new PolynomialFunction(new double[] { 0, 2, 3 }), "2 x + 3 x^2"); checkPolynomial(new PolynomialFunction(new double[] { 1, 2, 3 }), "1 + 2 x + 3 x^2"); checkPolynomial(new PolynomialFunction(new double[] { 1, 0, 3 }), "1 + 3 x^2"); checkPolynomial(new PolynomialFunction(new double[] { 0 }), "0"); } @Test public void testAddition() { PolynomialFunction p1 = new PolynomialFunction(new double[] { -2, 1 }); PolynomialFunction p2 = new PolynomialFunction(new double[] { 2, -1, 0 }); checkNullPolynomial(p1.add(p2)); p2 = p1.add(p1); checkPolynomial(p2, "-4 + 2 x"); p1 = new PolynomialFunction(new double[] { 1, -4, 2 }); p2 = new PolynomialFunction(new double[] { -1, 3, -2 }); p1 = p1.add(p2); Assert.assertEquals(1, p1.degree()); checkPolynomial(p1, "-x"); } @Test public void testSubtraction() { PolynomialFunction p1 = new PolynomialFunction(new double[] { -2, 1 }); checkNullPolynomial(p1.subtract(p1)); PolynomialFunction p2 = new PolynomialFunction(new double[] { -2, 6 }); p2 = p2.subtract(p1); checkPolynomial(p2, "5 x"); p1 = new PolynomialFunction(new double[] { 1, -4, 2 }); p2 = new PolynomialFunction(new double[] { -1, 3, 2 }); p1 = p1.subtract(p2); Assert.assertEquals(1, p1.degree()); checkPolynomial(p1, "2 - 7 x"); } @Test public void testMultiplication() { PolynomialFunction p1 = new PolynomialFunction(new double[] { -3, 2 }); PolynomialFunction p2 = new PolynomialFunction(new double[] { 3, 2, 1 }); checkPolynomial(p1.multiply(p2), "-9 + x^2 + 2 x^3"); p1 = new PolynomialFunction(new double[] { 0, 1 }); p2 = p1; for (int i = 2; i < 10; ++i) { p2 = p2.multiply(p1); checkPolynomial(p2, "x^" + i); } } @Test public void testSerial() { PolynomialFunction p2 = new PolynomialFunction(new double[] { 3, 2, 1 }); Assert.assertEquals(p2, TestUtils.serializeAndRecover(p2)); } /** * tests the firstDerivative function by comparison * * <p>This will test the functions * {@code f(x) = x^3 - 2x^2 + 6x + 3, g(x) = 3x^2 - 4x + 6} * and {@code h(x) = 6x - 4} */ @Test public void testMath341() { double[] f_coeff = { 3, 6, -2, 1 }; double[] g_coeff = { 6, -4, 3 }; double[] h_coeff = { -4, 6 }; PolynomialFunction f = new PolynomialFunction(f_coeff); PolynomialFunction g = new PolynomialFunction(g_coeff); PolynomialFunction h = new PolynomialFunction(h_coeff); // compare f' = g Assert.assertEquals(f.derivative().value(0), g.value(0), tolerance); Assert.assertEquals(f.derivative().value(1), g.value(1), tolerance); Assert.assertEquals(f.derivative().value(100), g.value(100), tolerance); Assert.assertEquals(f.derivative().value(4.1), g.value(4.1), tolerance); Assert.assertEquals(f.derivative().value(-3.25), g.value(-3.25), tolerance); // compare g' = h Assert.assertEquals(g.derivative().value(FastMath.PI), h.value(FastMath.PI), tolerance); Assert.assertEquals(g.derivative().value(FastMath.E), h.value(FastMath.E), tolerance); } public void checkPolynomial(PolynomialFunction p, String reference) { Assert.assertEquals(reference, p.toString()); } private void checkNullPolynomial(PolynomialFunction p) { for (double coefficient : p.getCoefficients()) { Assert.assertEquals(0, coefficient, 1e-15); } } }

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