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Commons Math example source code file (PolynomialsUtilsTest.java)
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); } } } Other Commons Math examples (source code examples)Here is a short list of links related to this Commons Math PolynomialsUtilsTest.java source code file: |
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