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.special; 018 019 import org.apache.commons.math.MathException; 020 import org.apache.commons.math.util.FastMath; 021 022 /** 023 * This is a utility class that provides computation methods related to the 024 * error functions. 025 * 026 * @version $Revision: 1054186 $ $Date: 2011-01-01 03:28:46 +0100 (sam. 01 janv. 2011) $ 027 */ 028 public class Erf { 029 030 /** 031 * Default constructor. Prohibit instantiation. 032 */ 033 private Erf() { 034 super(); 035 } 036 037 /** 038 * <p>Returns the error function</p> 039 * <p>erf(x) = 2/√π <sub>0</sub>∫<sup>x</sup> e<sup>-t<sup>2</sup></sup>dt </p> 040 * 041 * <p>This implementation computes erf(x) using the 042 * {@link Gamma#regularizedGammaP(double, double, double, int) regularized gamma function}, 043 * following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3)</p> 044 * 045 * <p>The value returned is always between -1 and 1 (inclusive). If {@code abs(x) > 40}, then 046 * {@code erf(x)} is indistinguishable from either 1 or -1 as a double, so the appropriate extreme 047 * value is returned.</p> 048 * 049 * @param x the value. 050 * @return the error function erf(x) 051 * @throws MathException if the algorithm fails to converge. 052 * @see Gamma#regularizedGammaP(double, double, double, int) 053 */ 054 public static double erf(double x) throws MathException { 055 if (FastMath.abs(x) > 40) { 056 return x > 0 ? 1 : -1; 057 } 058 double ret = Gamma.regularizedGammaP(0.5, x * x, 1.0e-15, 10000); 059 if (x < 0) { 060 ret = -ret; 061 } 062 return ret; 063 } 064 065 /** 066 * <p>Returns the complementary error function</p> 067 * <p>erfc(x) = 2/√π <sub>x</sub>∫<sup>∞</sup> e<sup>-t<sup>2</sup></sup>dt <br/> 068 * = 1 - {@link #erf(double) erf(x)} </p> 069 * 070 * <p>This implementation computes erfc(x) using the 071 * {@link Gamma#regularizedGammaQ(double, double, double, int) regularized gamma function}, 072 * following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3).</p> 073 * 074 * <p>The value returned is always between 0 and 2 (inclusive). If {@code abs(x) > 40}, then 075 * {@code erf(x)} is indistinguishable from either 0 or 2 as a double, so the appropriate extreme 076 * value is returned.</p> 077 * 078 * @param x the value 079 * @return the complementary error function erfc(x) 080 * @throws MathException if the algorithm fails to converge 081 * @see Gamma#regularizedGammaQ(double, double, double, int) 082 * @since 2.2 083 */ 084 public static double erfc(double x) throws MathException { 085 if (FastMath.abs(x) > 40) { 086 return x > 0 ? 0 : 2; 087 } 088 final double ret = Gamma.regularizedGammaQ(0.5, x * x, 1.0e-15, 10000); 089 return x < 0 ? 2 - ret : ret; 090 } 091 } 092