1 /* 2 * Licensed to the Apache Software Foundation (ASF) under one or more 3 * contributor license agreements. See the NOTICE file distributed with 4 * this work for additional information regarding copyright ownership. 5 * The ASF licenses this file to You under the Apache License, Version 2.0 6 * (the "License"); you may not use this file except in compliance with 7 * the License. You may obtain a copy of the License at 8 * 9 * http://www.apache.org/licenses/LICENSE-2.0 10 * 11 * Unless required by applicable law or agreed to in writing, software 12 * distributed under the License is distributed on an "AS IS" BASIS, 13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 * See the License for the specific language governing permissions and 15 * limitations under the License. 16 */ 17 package org.apache.commons.math.special; 18 19 import org.apache.commons.math.MathException; 20 import org.apache.commons.math.util.FastMath; 21 22 /** 23 * This is a utility class that provides computation methods related to the 24 * error functions. 25 * 26 * @version $Revision: 1054186 $ $Date: 2011-01-01 03:28:46 +0100 (sam. 01 janv. 2011) $ 27 */ 28 public class Erf { 29 30 /** 31 * Default constructor. Prohibit instantiation. 32 */ Erf()33 private Erf() { 34 super(); 35 } 36 37 /** 38 * <p>Returns the error function</p> 39 * <p>erf(x) = 2/√π <sub>0</sub>∫<sup>x</sup> e<sup>-t<sup>2</sup></sup>dt </p> 40 * 41 * <p>This implementation computes erf(x) using the 42 * {@link Gamma#regularizedGammaP(double, double, double, int) regularized gamma function}, 43 * following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3)</p> 44 * 45 * <p>The value returned is always between -1 and 1 (inclusive). If {@code abs(x) > 40}, then 46 * {@code erf(x)} is indistinguishable from either 1 or -1 as a double, so the appropriate extreme 47 * value is returned.</p> 48 * 49 * @param x the value. 50 * @return the error function erf(x) 51 * @throws MathException if the algorithm fails to converge. 52 * @see Gamma#regularizedGammaP(double, double, double, int) 53 */ erf(double x)54 public static double erf(double x) throws MathException { 55 if (FastMath.abs(x) > 40) { 56 return x > 0 ? 1 : -1; 57 } 58 double ret = Gamma.regularizedGammaP(0.5, x * x, 1.0e-15, 10000); 59 if (x < 0) { 60 ret = -ret; 61 } 62 return ret; 63 } 64 65 /** 66 * <p>Returns the complementary error function</p> 67 * <p>erfc(x) = 2/√π <sub>x</sub>∫<sup>∞</sup> e<sup>-t<sup>2</sup></sup>dt <br/> 68 * = 1 - {@link #erf(double) erf(x)} </p> 69 * 70 * <p>This implementation computes erfc(x) using the 71 * {@link Gamma#regularizedGammaQ(double, double, double, int) regularized gamma function}, 72 * following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3).</p> 73 * 74 * <p>The value returned is always between 0 and 2 (inclusive). If {@code abs(x) > 40}, then 75 * {@code erf(x)} is indistinguishable from either 0 or 2 as a double, so the appropriate extreme 76 * value is returned.</p> 77 * 78 * @param x the value 79 * @return the complementary error function erfc(x) 80 * @throws MathException if the algorithm fails to converge 81 * @see Gamma#regularizedGammaQ(double, double, double, int) 82 * @since 2.2 83 */ erfc(double x)84 public static double erfc(double x) throws MathException { 85 if (FastMath.abs(x) > 40) { 86 return x > 0 ? 0 : 2; 87 } 88 final double ret = Gamma.regularizedGammaQ(0.5, x * x, 1.0e-15, 10000); 89 return x < 0 ? 2 - ret : ret; 90 } 91 } 92 93