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Diffstat (limited to 'src/main/java/org/apache/commons/math/special/Erf.java')
| -rw-r--r-- | src/main/java/org/apache/commons/math/special/Erf.java | 92 |
1 files changed, 92 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math/special/Erf.java b/src/main/java/org/apache/commons/math/special/Erf.java new file mode 100644 index 0000000..5abe18b --- /dev/null +++ b/src/main/java/org/apache/commons/math/special/Erf.java @@ -0,0 +1,92 @@ +/* + * 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; + } +} + |