Class is obsolete.
Project: http://git-wip-us.apache.org/repos/asf/commons-math/repo Commit: http://git-wip-us.apache.org/repos/asf/commons-math/commit/87f6b2c3 Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/87f6b2c3 Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/87f6b2c3 Branch: refs/heads/master Commit: 87f6b2c3d2a7c4bfef8c64dc0ffe3da7815834e0 Parents: ef84681 Author: Gilles <er...@apache.org> Authored: Thu Jan 25 18:40:55 2018 +0100 Committer: Gilles <er...@apache.org> Committed: Thu Jan 25 18:40:55 2018 +0100 ---------------------------------------------------------------------- .../distribution/SaddlePointExpansion.java | 206 ------------------- 1 file changed, 206 deletions(-) ---------------------------------------------------------------------- http://git-wip-us.apache.org/repos/asf/commons-math/blob/87f6b2c3/src/main/java/org/apache/commons/math4/distribution/SaddlePointExpansion.java ---------------------------------------------------------------------- diff --git a/src/main/java/org/apache/commons/math4/distribution/SaddlePointExpansion.java b/src/main/java/org/apache/commons/math4/distribution/SaddlePointExpansion.java deleted file mode 100644 index 7def8fb..0000000 --- a/src/main/java/org/apache/commons/math4/distribution/SaddlePointExpansion.java +++ /dev/null @@ -1,206 +0,0 @@ -/* - * 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.math4.distribution; - -import org.apache.commons.numbers.gamma.LogGamma; -import org.apache.commons.math4.util.FastMath; -import org.apache.commons.math4.util.MathUtils; - -/** - * <p> - * Utility class used by various distributions to accurately compute their - * respective probability mass functions. The implementation for this class is - * based on the Catherine Loader's <a target="_blank" - * href="http://www.herine.net/stat/software/dbinom.html";>dbinom</a> routines. - * </p> - * <p> - * This class is not intended to be called directly. - * </p> - * <p> - * References: - * <ol> - * <li>Catherine Loader (2000). "Fast and Accurate Computation of Binomial - * Probabilities.". <a target="_blank" - * href="http://www.herine.net/stat/papers/dbinom.pdf";> - * http://www.herine.net/stat/papers/dbinom.pdf</a></li> - * </ol> - * </p> - * - * @since 2.1 - */ -final class SaddlePointExpansion { - - /** 1/2 * log(2 π). */ - private static final double HALF_LOG_2_PI = 0.5 * FastMath.log(MathUtils.TWO_PI); - - /** exact Stirling expansion error for certain values. */ - private static final double[] EXACT_STIRLING_ERRORS = { 0.0, /* 0.0 */ - 0.1534264097200273452913848, /* 0.5 */ - 0.0810614667953272582196702, /* 1.0 */ - 0.0548141210519176538961390, /* 1.5 */ - 0.0413406959554092940938221, /* 2.0 */ - 0.03316287351993628748511048, /* 2.5 */ - 0.02767792568499833914878929, /* 3.0 */ - 0.02374616365629749597132920, /* 3.5 */ - 0.02079067210376509311152277, /* 4.0 */ - 0.01848845053267318523077934, /* 4.5 */ - 0.01664469118982119216319487, /* 5.0 */ - 0.01513497322191737887351255, /* 5.5 */ - 0.01387612882307074799874573, /* 6.0 */ - 0.01281046524292022692424986, /* 6.5 */ - 0.01189670994589177009505572, /* 7.0 */ - 0.01110455975820691732662991, /* 7.5 */ - 0.010411265261972096497478567, /* 8.0 */ - 0.009799416126158803298389475, /* 8.5 */ - 0.009255462182712732917728637, /* 9.0 */ - 0.008768700134139385462952823, /* 9.5 */ - 0.008330563433362871256469318, /* 10.0 */ - 0.007934114564314020547248100, /* 10.5 */ - 0.007573675487951840794972024, /* 11.0 */ - 0.007244554301320383179543912, /* 11.5 */ - 0.006942840107209529865664152, /* 12.0 */ - 0.006665247032707682442354394, /* 12.5 */ - 0.006408994188004207068439631, /* 13.0 */ - 0.006171712263039457647532867, /* 13.5 */ - 0.005951370112758847735624416, /* 14.0 */ - 0.005746216513010115682023589, /* 14.5 */ - 0.005554733551962801371038690 /* 15.0 */ - }; - - /** - * Default constructor. - */ - private SaddlePointExpansion() { - super(); - } - - /** - * Compute the error of Stirling's series at the given value. - * <p> - * References: - * <ol> - * <li>Eric W. Weisstein. "Stirling's Series." From MathWorld--A Wolfram Web - * Resource. <a target="_blank" - * href="http://mathworld.wolfram.com/StirlingsSeries.html";> - * http://mathworld.wolfram.com/StirlingsSeries.html</a></li> - * </ol> - * </p> - * - * @param z the value. - * @return the Striling's series error. - */ - static double getStirlingError(double z) { - double ret; - if (z < 15.0) { - double z2 = 2.0 * z; - if (FastMath.floor(z2) == z2) { - ret = EXACT_STIRLING_ERRORS[(int) z2]; - } else { - ret = LogGamma.value(z + 1.0) - (z + 0.5) * FastMath.log(z) + - z - HALF_LOG_2_PI; - } - } else { - double z2 = z * z; - ret = (0.083333333333333333333 - - (0.00277777777777777777778 - - (0.00079365079365079365079365 - - (0.000595238095238095238095238 - - 0.0008417508417508417508417508 / - z2) / z2) / z2) / z2) / z; - } - return ret; - } - - /** - * A part of the deviance portion of the saddle point approximation. - * <p> - * References: - * <ol> - * <li>Catherine Loader (2000). "Fast and Accurate Computation of Binomial - * Probabilities.". <a target="_blank" - * href="http://www.herine.net/stat/papers/dbinom.pdf";> - * http://www.herine.net/stat/papers/dbinom.pdf</a></li> - * </ol> - * </p> - * - * @param x the x value. - * @param mu the average. - * @return a part of the deviance. - */ - static double getDeviancePart(double x, double mu) { - double ret; - if (FastMath.abs(x - mu) < 0.1 * (x + mu)) { - double d = x - mu; - double v = d / (x + mu); - double s1 = v * d; - double s = Double.NaN; - double ej = 2.0 * x * v; - v *= v; - int j = 1; - while (s1 != s) { - s = s1; - ej *= v; - s1 = s + ej / ((j * 2) + 1); - ++j; - } - ret = s1; - } else { - if (x == 0) { - return mu; - } - ret = x * FastMath.log(x / mu) + mu - x; - } - return ret; - } - - /** - * Compute the logarithm of the PMF for a binomial distribution - * using the saddle point expansion. - * - * @param x the value at which the probability is evaluated. - * @param n the number of trials. - * @param p the probability of success. - * @param q the probability of failure (1 - p). - * @return log(p(x)). - */ - static double logBinomialProbability(int x, int n, double p, double q) { - double ret; - if (x == 0) { - if (p < 0.1) { - ret = -getDeviancePart(n, n * q) - n * p; - } else { - if (n == 0) { - return 0; - } - ret = n * FastMath.log(q); - } - } else if (x == n) { - if (q < 0.1) { - ret = -getDeviancePart(n, n * p) - n * q; - } else { - ret = n * FastMath.log(p); - } - } else { - ret = getStirlingError(n) - getStirlingError(x) - - getStirlingError(n - x) - getDeviancePart(x, n * p) - - getDeviancePart(n - x, n * q); - double f = (MathUtils.TWO_PI * x * (n - x)) / n; - ret = -0.5 * FastMath.log(f) + ret; - } - return ret; - } -}
