| /* |
| * 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.numbers.gamma; |
| |
| /** |
| * <a href="http://en.wikipedia.org/wiki/Trigamma_function">Trigamma function</a>. |
| * |
| * It is the derivative of the {@link Digamma digamma function}: |
| * \( \psi_1(x) = \frac{d^2}{dx^2} (\ln \Gamma(x)) \). |
| */ |
| public final class Trigamma { |
| /** C limit. */ |
| private static final double C_LIMIT = 49; |
| |
| /** S limit. */ |
| private static final double S_LIMIT = 1e-5; |
| /** Fraction. */ |
| private static final double F_1_6 = 1d / 6; |
| /** Fraction. */ |
| private static final double F_1_30 = 1d / 30; |
| /** Fraction. */ |
| private static final double F_1_42 = 1d / 42; |
| |
| /** Private constructor. */ |
| private Trigamma() { |
| // intentional empty. |
| } |
| |
| /** |
| * Computes the trigamma function. |
| * |
| * @param x Argument. |
| * @return trigamma(x) to within {@code 1e-8} relative or absolute error whichever is larger. |
| */ |
| public static double value(double x) { |
| if (Double.isNaN(x) || Double.isInfinite(x)) { |
| return x; |
| } |
| |
| if (x > 0 && x <= S_LIMIT) { |
| return 1 / (x * x); |
| } |
| |
| if (x >= C_LIMIT) { |
| final double inv = 1 / (x * x); |
| // 1 1 1 1 1 |
| // - + ---- + ---- - ----- + ----- |
| // x 2 3 5 7 |
| // 2 x 6 x 30 x 42 x |
| return 1 / x + inv / 2 + inv / x * (F_1_6 - inv * (F_1_30 + F_1_42 * inv)); |
| } |
| |
| return value(x + 1) + 1 / (x * x); |
| } |
| } |