Classes in this File | Line Coverage | Branch Coverage | Complexity | ||||||||
ContinuedFraction |
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| 2.0;2 |
1 | /* |
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2 | * Copyright 2003-2004 The Apache Software Foundation. |
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3 | * |
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4 | * Licensed under the Apache License, Version 2.0 (the "License"); |
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5 | * you may not use this file except in compliance with the License. |
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6 | * You may obtain a copy of the License at |
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7 | * |
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8 | * http://www.apache.org/licenses/LICENSE-2.0 |
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9 | * |
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10 | * Unless required by applicable law or agreed to in writing, software |
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11 | * distributed under the License is distributed on an "AS IS" BASIS, |
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12 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
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13 | * See the License for the specific language governing permissions and |
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14 | * limitations under the License. |
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15 | */ |
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16 | package org.apache.commons.math.util; |
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17 | ||
18 | import java.io.Serializable; |
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19 | ||
20 | import org.apache.commons.math.ConvergenceException; |
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21 | import org.apache.commons.math.MathException; |
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22 | ||
23 | /** |
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24 | * Provides a generic means to evaluate continued fractions. Subclasses simply |
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25 | * provided the a and b coefficients to evaluate the continued fraction. |
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26 | * |
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27 | * <p> |
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28 | * References: |
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29 | * <ul> |
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30 | * <li><a href="http://mathworld.wolfram.com/ContinuedFraction.html"> |
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31 | * Continued Fraction</a></li> |
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32 | * </ul> |
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33 | * </p> |
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34 | * |
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35 | * @version $Revision$ $Date: 2005-08-22 19:27:17 -0700 (Mon, 22 Aug 2005) $ |
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36 | */ |
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37 | public abstract class ContinuedFraction implements Serializable { |
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38 | ||
39 | /** Serialization UID */ |
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40 | static final long serialVersionUID = 1768555336266158242L; |
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41 | ||
42 | /** Maximum allowed numerical error. */ |
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43 | private static final double DEFAULT_EPSILON = 10e-9; |
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44 | ||
45 | /** |
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46 | * Default constructor. |
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47 | */ |
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48 | protected ContinuedFraction() { |
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49 | 6282 | super(); |
50 | 6282 | } |
51 | ||
52 | /** |
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53 | * Access the n-th a coefficient of the continued fraction. Since a can be |
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54 | * a function of the evaluation point, x, that is passed in as well. |
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55 | * @param n the coefficient index to retrieve. |
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56 | * @param x the evaluation point. |
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57 | * @return the n-th a coefficient. |
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58 | */ |
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59 | protected abstract double getA(int n, double x); |
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60 | ||
61 | /** |
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62 | * Access the n-th b coefficient of the continued fraction. Since b can be |
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63 | * a function of the evaluation point, x, that is passed in as well. |
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64 | * @param n the coefficient index to retrieve. |
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65 | * @param x the evaluation point. |
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66 | * @return the n-th b coefficient. |
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67 | */ |
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68 | protected abstract double getB(int n, double x); |
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69 | ||
70 | /** |
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71 | * Evaluates the continued fraction at the value x. |
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72 | * @param x the evaluation point. |
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73 | * @return the value of the continued fraction evaluated at x. |
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74 | * @throws MathException if the algorithm fails to converge. |
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75 | */ |
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76 | public double evaluate(double x) throws MathException { |
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77 | 0 | return evaluate(x, DEFAULT_EPSILON, Integer.MAX_VALUE); |
78 | } |
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79 | ||
80 | /** |
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81 | * Evaluates the continued fraction at the value x. |
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82 | * @param x the evaluation point. |
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83 | * @param epsilon maximum error allowed. |
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84 | * @return the value of the continued fraction evaluated at x. |
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85 | * @throws MathException if the algorithm fails to converge. |
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86 | */ |
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87 | public double evaluate(double x, double epsilon) throws MathException { |
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88 | 2 | return evaluate(x, epsilon, Integer.MAX_VALUE); |
89 | } |
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90 | ||
91 | /** |
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92 | * Evaluates the continued fraction at the value x. |
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93 | * @param x the evaluation point. |
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94 | * @param maxIterations maximum number of convergents |
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95 | * @return the value of the continued fraction evaluated at x. |
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96 | * @throws MathException if the algorithm fails to converge. |
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97 | */ |
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98 | public double evaluate(double x, int maxIterations) throws MathException { |
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99 | 0 | return evaluate(x, DEFAULT_EPSILON, maxIterations); |
100 | } |
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101 | ||
102 | /** |
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103 | * <p> |
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104 | * Evaluates the continued fraction at the value x. |
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105 | * </p> |
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106 | * |
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107 | * <p> |
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108 | * The implementation of this method is based on equations 14-17 of: |
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109 | * <ul> |
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110 | * <li> |
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111 | * Eric W. Weisstein. "Continued Fraction." From MathWorld--A Wolfram Web |
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112 | * Resource. <a target="_blank" |
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113 | * href="http://mathworld.wolfram.com/ContinuedFraction.html"> |
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114 | * http://mathworld.wolfram.com/ContinuedFraction.html</a> |
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115 | * </li> |
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116 | * </ul> |
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117 | * The recurrence relationship defined in those equations can result in |
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118 | * very large intermediate results which can result in numerical overflow. |
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119 | * As a means to combat these overflow conditions, the intermediate results |
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120 | * are scaled whenever they threaten to become numerically unstable. |
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121 | * |
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122 | * @param x the evaluation point. |
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123 | * @param epsilon maximum error allowed. |
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124 | * @param maxIterations maximum number of convergents |
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125 | * @return the value of the continued fraction evaluated at x. |
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126 | * @throws MathException if the algorithm fails to converge. |
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127 | */ |
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128 | public double evaluate(double x, double epsilon, int maxIterations) |
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129 | throws MathException |
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130 | { |
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131 | 6282 | double p0 = 1.0; |
132 | 6282 | double p1 = getA(0, x); |
133 | 6282 | double q0 = 0.0; |
134 | 6282 | double q1 = 1.0; |
135 | 6282 | double c = p1 / q1; |
136 | 6282 | int n = 0; |
137 | 6282 | double relativeError = Double.MAX_VALUE; |
138 | 65950 | while (n < maxIterations && relativeError > epsilon) { |
139 | 59668 | ++n; |
140 | 59668 | double a = getA(n, x); |
141 | 59668 | double b = getB(n, x); |
142 | 59668 | double p2 = a * p1 + b * p0; |
143 | 59668 | double q2 = a * q1 + b * q0; |
144 | 59668 | if (Double.isInfinite(p2) || Double.isInfinite(q2)) { |
145 | // need to scale |
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146 | 628 | if (a != 0.0) { |
147 | 628 | p2 = p1 + (b / a * p0); |
148 | 628 | q2 = q1 + (b / a * q0); |
149 | 0 | } else if (b != 0) { |
150 | 0 | p2 = (a / b * p1) + p0; |
151 | 0 | q2 = (a / b * q1) + q0; |
152 | } else { |
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153 | // can not scale an convergent is unbounded. |
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154 | 0 | throw new ConvergenceException( |
155 | "Continued fraction convergents diverged to +/- " + |
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156 | "infinity."); |
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157 | } |
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158 | } |
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159 | 59668 | double r = p2 / q2; |
160 | 59668 | relativeError = Math.abs(r / c - 1.0); |
161 | ||
162 | // prepare for next iteration |
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163 | 59668 | c = p2 / q2; |
164 | 59668 | p0 = p1; |
165 | 59668 | p1 = p2; |
166 | 59668 | q0 = q1; |
167 | 59668 | q1 = q2; |
168 | } |
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169 | ||
170 | 6282 | if (n >= maxIterations) { |
171 | 0 | throw new ConvergenceException( |
172 | "Continued fraction convergents failed to converge."); |
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173 | } |
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174 | ||
175 | 6282 | return c; |
176 | } |
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177 | } |