001 /* 002 * Licensed to the Apache Software Foundation (ASF) under one or more 003 * contributor license agreements. See the NOTICE file distributed with 004 * this work for additional information regarding copyright ownership. 005 * The ASF licenses this file to You under the Apache License, Version 2.0 006 * (the "License"); you may not use this file except in compliance with 007 * the License. You may obtain a copy of the License at 008 * 009 * http://www.apache.org/licenses/LICENSE-2.0 010 * 011 * Unless required by applicable law or agreed to in writing, software 012 * distributed under the License is distributed on an "AS IS" BASIS, 013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 014 * See the License for the specific language governing permissions and 015 * limitations under the License. 016 */ 017 package org.apache.commons.math.analysis.interpolation; 018 019 import org.apache.commons.math.MathException; 020 import org.apache.commons.math.analysis.Expm1Function; 021 import org.apache.commons.math.analysis.SinFunction; 022 import org.apache.commons.math.analysis.UnivariateRealFunction; 023 024 import junit.framework.TestCase; 025 026 /** 027 * Testcase for Neville interpolator. 028 * <p> 029 * The error of polynomial interpolation is 030 * f(z) - p(z) = f^(n)(zeta) * (z-x[0])(z-x[1])...(z-x[n-1]) / n! 031 * where f^(n) is the n-th derivative of the approximated function and 032 * zeta is some point in the interval determined by x[] and z. 033 * <p> 034 * Since zeta is unknown, f^(n)(zeta) cannot be calculated. But we can bound 035 * it and use the absolute value upper bound for estimates. For reference, 036 * see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X, chapter 2. 037 * 038 * @version $Revision: 799857 $ $Date: 2009-08-01 09:07:12 -0400 (Sat, 01 Aug 2009) $ 039 */ 040 public final class NevilleInterpolatorTest extends TestCase { 041 042 /** 043 * Test of interpolator for the sine function. 044 * <p> 045 * |sin^(n)(zeta)| <= 1.0, zeta in [0, 2*PI] 046 */ 047 public void testSinFunction() throws MathException { 048 UnivariateRealFunction f = new SinFunction(); 049 UnivariateRealInterpolator interpolator = new NevilleInterpolator(); 050 double x[], y[], z, expected, result, tolerance; 051 052 // 6 interpolating points on interval [0, 2*PI] 053 int n = 6; 054 double min = 0.0, max = 2 * Math.PI; 055 x = new double[n]; 056 y = new double[n]; 057 for (int i = 0; i < n; i++) { 058 x[i] = min + i * (max - min) / n; 059 y[i] = f.value(x[i]); 060 } 061 double derivativebound = 1.0; 062 UnivariateRealFunction p = interpolator.interpolate(x, y); 063 064 z = Math.PI / 4; expected = f.value(z); result = p.value(z); 065 tolerance = Math.abs(derivativebound * partialerror(x, z)); 066 assertEquals(expected, result, tolerance); 067 068 z = Math.PI * 1.5; expected = f.value(z); result = p.value(z); 069 tolerance = Math.abs(derivativebound * partialerror(x, z)); 070 assertEquals(expected, result, tolerance); 071 } 072 073 /** 074 * Test of interpolator for the exponential function. 075 * <p> 076 * |expm1^(n)(zeta)| <= e, zeta in [-1, 1] 077 */ 078 public void testExpm1Function() throws MathException { 079 UnivariateRealFunction f = new Expm1Function(); 080 UnivariateRealInterpolator interpolator = new NevilleInterpolator(); 081 double x[], y[], z, expected, result, tolerance; 082 083 // 5 interpolating points on interval [-1, 1] 084 int n = 5; 085 double min = -1.0, max = 1.0; 086 x = new double[n]; 087 y = new double[n]; 088 for (int i = 0; i < n; i++) { 089 x[i] = min + i * (max - min) / n; 090 y[i] = f.value(x[i]); 091 } 092 double derivativebound = Math.E; 093 UnivariateRealFunction p = interpolator.interpolate(x, y); 094 095 z = 0.0; expected = f.value(z); result = p.value(z); 096 tolerance = Math.abs(derivativebound * partialerror(x, z)); 097 assertEquals(expected, result, tolerance); 098 099 z = 0.5; expected = f.value(z); result = p.value(z); 100 tolerance = Math.abs(derivativebound * partialerror(x, z)); 101 assertEquals(expected, result, tolerance); 102 103 z = -0.5; expected = f.value(z); result = p.value(z); 104 tolerance = Math.abs(derivativebound * partialerror(x, z)); 105 assertEquals(expected, result, tolerance); 106 } 107 108 /** 109 * Test of parameters for the interpolator. 110 */ 111 public void testParameters() throws Exception { 112 UnivariateRealInterpolator interpolator = new NevilleInterpolator(); 113 114 try { 115 // bad abscissas array 116 double x[] = { 1.0, 2.0, 2.0, 4.0 }; 117 double y[] = { 0.0, 4.0, 4.0, 2.5 }; 118 UnivariateRealFunction p = interpolator.interpolate(x, y); 119 p.value(0.0); 120 fail("Expecting MathException - bad abscissas array"); 121 } catch (MathException ex) { 122 // expected 123 } 124 } 125 126 /** 127 * Returns the partial error term (z-x[0])(z-x[1])...(z-x[n-1])/n! 128 */ 129 protected double partialerror(double x[], double z) throws 130 IllegalArgumentException { 131 132 if (x.length < 1) { 133 throw new IllegalArgumentException 134 ("Interpolation array cannot be empty."); 135 } 136 double out = 1; 137 for (int i = 0; i < x.length; i++) { 138 out *= (z - x[i]) / (i + 1); 139 } 140 return out; 141 } 142 }