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/&radic;&pi; <sub>0</sub>&int;<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/&radic;&pi; <sub>x</sub>&int;<sup>&infin;</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