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Commons Math example source code file (PolynomialsUtilsTest.java)

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

Java - Commons Math tags/keywords

hk0, hk1, hk2, lk0, lk0g0, lk1, lk1g1, pk1g1, pk1g1, polynomialfunction, polynomialfunction, string, string, testcase

The Commons Math PolynomialsUtilsTest.java 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.math.analysis.polynomials;

import junit.framework.TestCase;

/**
 * Tests the PolynomialsUtils class.
 *
 * @version $Revision: 761213 $ $Date: 2009-04-02 05:05:56 -0400 (Thu, 02 Apr 2009) $
 */
public class PolynomialsUtilsTest extends TestCase {

    public void testFirstChebyshevPolynomials() {

        checkPolynomial(PolynomialsUtils.createChebyshevPolynomial(3), "-3.0 x + 4.0 x^3");
        checkPolynomial(PolynomialsUtils.createChebyshevPolynomial(2), "-1.0 + 2.0 x^2");
        checkPolynomial(PolynomialsUtils.createChebyshevPolynomial(1), "x");
        checkPolynomial(PolynomialsUtils.createChebyshevPolynomial(0), "1.0");

        checkPolynomial(PolynomialsUtils.createChebyshevPolynomial(7), "-7.0 x + 56.0 x^3 - 112.0 x^5 + 64.0 x^7");
        checkPolynomial(PolynomialsUtils.createChebyshevPolynomial(6), "-1.0 + 18.0 x^2 - 48.0 x^4 + 32.0 x^6");
        checkPolynomial(PolynomialsUtils.createChebyshevPolynomial(5), "5.0 x - 20.0 x^3 + 16.0 x^5");
        checkPolynomial(PolynomialsUtils.createChebyshevPolynomial(4), "1.0 - 8.0 x^2 + 8.0 x^4");

    }

    public void testChebyshevBounds() {
        for (int k = 0; k < 12; ++k) {
            PolynomialFunction Tk = PolynomialsUtils.createChebyshevPolynomial(k);
            for (double x = -1.0; x <= 1.0; x += 0.02) {
                assertTrue(k + " " + Tk.value(x), Math.abs(Tk.value(x)) < (1.0 + 1.0e-12));
            }
        }
    }

    public void testChebyshevDifferentials() {
        for (int k = 0; k < 12; ++k) {

            PolynomialFunction Tk0 = PolynomialsUtils.createChebyshevPolynomial(k);
            PolynomialFunction Tk1 = Tk0.polynomialDerivative();
            PolynomialFunction Tk2 = Tk1.polynomialDerivative();

            PolynomialFunction g0 = new PolynomialFunction(new double[] { k * k });
            PolynomialFunction g1 = new PolynomialFunction(new double[] { 0, -1});
            PolynomialFunction g2 = new PolynomialFunction(new double[] { 1, 0, -1 });

            PolynomialFunction Tk0g0 = Tk0.multiply(g0);
            PolynomialFunction Tk1g1 = Tk1.multiply(g1);
            PolynomialFunction Tk2g2 = Tk2.multiply(g2);

            checkNullPolynomial(Tk0g0.add(Tk1g1.add(Tk2g2)));

        }
    }

    public void testFirstHermitePolynomials() {

        checkPolynomial(PolynomialsUtils.createHermitePolynomial(3), "-12.0 x + 8.0 x^3");
        checkPolynomial(PolynomialsUtils.createHermitePolynomial(2), "-2.0 + 4.0 x^2");
        checkPolynomial(PolynomialsUtils.createHermitePolynomial(1), "2.0 x");
        checkPolynomial(PolynomialsUtils.createHermitePolynomial(0), "1.0");

        checkPolynomial(PolynomialsUtils.createHermitePolynomial(7), "-1680.0 x + 3360.0 x^3 - 1344.0 x^5 + 128.0 x^7");
        checkPolynomial(PolynomialsUtils.createHermitePolynomial(6), "-120.0 + 720.0 x^2 - 480.0 x^4 + 64.0 x^6");
        checkPolynomial(PolynomialsUtils.createHermitePolynomial(5), "120.0 x - 160.0 x^3 + 32.0 x^5");
        checkPolynomial(PolynomialsUtils.createHermitePolynomial(4), "12.0 - 48.0 x^2 + 16.0 x^4");

    }

    public void testHermiteDifferentials() {
        for (int k = 0; k < 12; ++k) {

            PolynomialFunction Hk0 = PolynomialsUtils.createHermitePolynomial(k);
            PolynomialFunction Hk1 = Hk0.polynomialDerivative();
            PolynomialFunction Hk2 = Hk1.polynomialDerivative();

            PolynomialFunction g0 = new PolynomialFunction(new double[] { 2 * k });
            PolynomialFunction g1 = new PolynomialFunction(new double[] { 0, -2 });
            PolynomialFunction g2 = new PolynomialFunction(new double[] { 1 });

            PolynomialFunction Hk0g0 = Hk0.multiply(g0);
            PolynomialFunction Hk1g1 = Hk1.multiply(g1);
            PolynomialFunction Hk2g2 = Hk2.multiply(g2);

            checkNullPolynomial(Hk0g0.add(Hk1g1.add(Hk2g2)));

        }
    }

    public void testFirstLaguerrePolynomials() {

        checkPolynomial(PolynomialsUtils.createLaguerrePolynomial(3), 6l, "6.0 - 18.0 x + 9.0 x^2 - x^3");
        checkPolynomial(PolynomialsUtils.createLaguerrePolynomial(2), 2l, "2.0 - 4.0 x + x^2");
        checkPolynomial(PolynomialsUtils.createLaguerrePolynomial(1), 1l, "1.0 - x");
        checkPolynomial(PolynomialsUtils.createLaguerrePolynomial(0), 1l, "1.0");

        checkPolynomial(PolynomialsUtils.createLaguerrePolynomial(7), 5040l,
                "5040.0 - 35280.0 x + 52920.0 x^2 - 29400.0 x^3"
                + " + 7350.0 x^4 - 882.0 x^5 + 49.0 x^6 - x^7");
        checkPolynomial(PolynomialsUtils.createLaguerrePolynomial(6),  720l,
                "720.0 - 4320.0 x + 5400.0 x^2 - 2400.0 x^3 + 450.0 x^4"
                + " - 36.0 x^5 + x^6");
        checkPolynomial(PolynomialsUtils.createLaguerrePolynomial(5),  120l,
        "120.0 - 600.0 x + 600.0 x^2 - 200.0 x^3 + 25.0 x^4 - x^5");
        checkPolynomial(PolynomialsUtils.createLaguerrePolynomial(4),   24l,
        "24.0 - 96.0 x + 72.0 x^2 - 16.0 x^3 + x^4");

    }

    public void testLaguerreDifferentials() {
        for (int k = 0; k < 12; ++k) {

            PolynomialFunction Lk0 = PolynomialsUtils.createLaguerrePolynomial(k);
            PolynomialFunction Lk1 = Lk0.polynomialDerivative();
            PolynomialFunction Lk2 = Lk1.polynomialDerivative();

            PolynomialFunction g0 = new PolynomialFunction(new double[] { k });
            PolynomialFunction g1 = new PolynomialFunction(new double[] { 1, -1 });
            PolynomialFunction g2 = new PolynomialFunction(new double[] { 0, 1 });

            PolynomialFunction Lk0g0 = Lk0.multiply(g0);
            PolynomialFunction Lk1g1 = Lk1.multiply(g1);
            PolynomialFunction Lk2g2 = Lk2.multiply(g2);

            checkNullPolynomial(Lk0g0.add(Lk1g1.add(Lk2g2)));

        }
    }

    public void testFirstLegendrePolynomials() {

        checkPolynomial(PolynomialsUtils.createLegendrePolynomial(3),  2l, "-3.0 x + 5.0 x^3");
        checkPolynomial(PolynomialsUtils.createLegendrePolynomial(2),  2l, "-1.0 + 3.0 x^2");
        checkPolynomial(PolynomialsUtils.createLegendrePolynomial(1),  1l, "x");
        checkPolynomial(PolynomialsUtils.createLegendrePolynomial(0),  1l, "1.0");

        checkPolynomial(PolynomialsUtils.createLegendrePolynomial(7), 16l, "-35.0 x + 315.0 x^3 - 693.0 x^5 + 429.0 x^7");
        checkPolynomial(PolynomialsUtils.createLegendrePolynomial(6), 16l, "-5.0 + 105.0 x^2 - 315.0 x^4 + 231.0 x^6");
        checkPolynomial(PolynomialsUtils.createLegendrePolynomial(5),  8l, "15.0 x - 70.0 x^3 + 63.0 x^5");
        checkPolynomial(PolynomialsUtils.createLegendrePolynomial(4),  8l, "3.0 - 30.0 x^2 + 35.0 x^4");

    }

    public void testLegendreDifferentials() {
        for (int k = 0; k < 12; ++k) {

            PolynomialFunction Pk0 = PolynomialsUtils.createLegendrePolynomial(k);
            PolynomialFunction Pk1 = Pk0.polynomialDerivative();
            PolynomialFunction Pk2 = Pk1.polynomialDerivative();

            PolynomialFunction g0 = new PolynomialFunction(new double[] { k * (k + 1) });
            PolynomialFunction g1 = new PolynomialFunction(new double[] { 0, -2 });
            PolynomialFunction g2 = new PolynomialFunction(new double[] { 1, 0, -1 });

            PolynomialFunction Pk0g0 = Pk0.multiply(g0);
            PolynomialFunction Pk1g1 = Pk1.multiply(g1);
            PolynomialFunction Pk2g2 = Pk2.multiply(g2);

            checkNullPolynomial(Pk0g0.add(Pk1g1.add(Pk2g2)));

        }
    }

    public void testHighDegreeLegendre() {
        PolynomialsUtils.createLegendrePolynomial(40);
        double[] l40 = PolynomialsUtils.createLegendrePolynomial(40).getCoefficients();
        double denominator = 274877906944.0;
        double[] numerators = new double[] {
                          +34461632205.0,            -28258538408100.0,          +3847870979902950.0,        -207785032914759300.0,
                  +5929294332103310025.0,     -103301483474866556880.0,    +1197358103913226000200.0,    -9763073770369381232400.0,
              +58171647881784229843050.0,  -260061484647976556945400.0,  +888315281771246239250340.0, -2345767627188139419665400.0,
            +4819022625419112503443050.0, -7710436200670580005508880.0, +9566652323054238154983240.0, -9104813935044723209570256.0,
            +6516550296251767619752905.0, -3391858621221953912598660.0, +1211378079007840683070950.0,  -265365894974690562152100.0,
              +26876802183334044115405.0
        };
        for (int i = 0; i < l40.length; ++i) {
            if (i % 2 == 0) {
                double ci = numerators[i / 2] / denominator;
                assertEquals(ci, l40[i], Math.abs(ci) * 1.0e-15);
            } else {
                assertEquals(0.0, l40[i], 0.0);
            }
        }
    }

    private void checkPolynomial(PolynomialFunction p, long denominator, String reference) {
        PolynomialFunction q = new PolynomialFunction(new double[] { denominator});
        assertEquals(reference, p.multiply(q).toString());
    }

    private void checkPolynomial(PolynomialFunction p, String reference) {
        assertEquals(reference, p.toString());
    }

    private void checkNullPolynomial(PolynomialFunction p) {
        for (double coefficient : p.getCoefficients()) {
            assertEquals(0.0, coefficient, 1.0e-13);
        }
    }

}

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