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