| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * this work for additional information regarding copyright ownership. |
| * The ASF licenses this file to You under the Apache License, Version 2.0 |
| * (the "License"); you may not use this file except in compliance with |
| * the License. You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| package org.apache.commons.math.special; |
| |
| import org.apache.commons.math.MathException; |
| import org.apache.commons.math.util.FastMath; |
| |
| /** |
| * This is a utility class that provides computation methods related to the |
| * error functions. |
| * |
| * @version $Revision: 1054186 $ $Date: 2011-01-01 03:28:46 +0100 (sam. 01 janv. 2011) $ |
| */ |
| public class Erf { |
| |
| /** |
| * Default constructor. Prohibit instantiation. |
| */ |
| private Erf() { |
| super(); |
| } |
| |
| /** |
| * <p>Returns the error function</p> |
| * <p>erf(x) = 2/√π <sub>0</sub>∫<sup>x</sup> e<sup>-t<sup>2</sup></sup>dt </p> |
| * |
| * <p>This implementation computes erf(x) using the |
| * {@link Gamma#regularizedGammaP(double, double, double, int) regularized gamma function}, |
| * following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3)</p> |
| * |
| * <p>The value returned is always between -1 and 1 (inclusive). If {@code abs(x) > 40}, then |
| * {@code erf(x)} is indistinguishable from either 1 or -1 as a double, so the appropriate extreme |
| * value is returned.</p> |
| * |
| * @param x the value. |
| * @return the error function erf(x) |
| * @throws MathException if the algorithm fails to converge. |
| * @see Gamma#regularizedGammaP(double, double, double, int) |
| */ |
| public static double erf(double x) throws MathException { |
| if (FastMath.abs(x) > 40) { |
| return x > 0 ? 1 : -1; |
| } |
| double ret = Gamma.regularizedGammaP(0.5, x * x, 1.0e-15, 10000); |
| if (x < 0) { |
| ret = -ret; |
| } |
| return ret; |
| } |
| |
| /** |
| * <p>Returns the complementary error function</p> |
| * <p>erfc(x) = 2/√π <sub>x</sub>∫<sup>∞</sup> e<sup>-t<sup>2</sup></sup>dt <br/> |
| * = 1 - {@link #erf(double) erf(x)} </p> |
| * |
| * <p>This implementation computes erfc(x) using the |
| * {@link Gamma#regularizedGammaQ(double, double, double, int) regularized gamma function}, |
| * following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3).</p> |
| * |
| * <p>The value returned is always between 0 and 2 (inclusive). If {@code abs(x) > 40}, then |
| * {@code erf(x)} is indistinguishable from either 0 or 2 as a double, so the appropriate extreme |
| * value is returned.</p> |
| * |
| * @param x the value |
| * @return the complementary error function erfc(x) |
| * @throws MathException if the algorithm fails to converge |
| * @see Gamma#regularizedGammaQ(double, double, double, int) |
| * @since 2.2 |
| */ |
| public static double erfc(double x) throws MathException { |
| if (FastMath.abs(x) > 40) { |
| return x > 0 ? 0 : 2; |
| } |
| final double ret = Gamma.regularizedGammaQ(0.5, x * x, 1.0e-15, 10000); |
| return x < 0 ? 2 - ret : ret; |
| } |
| } |
| |