org.apache.commons.numbers.gamma.LogGamma Maven / Gradle / Ivy
/*
* 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;
/**
* Function \( \ln \Gamma(x) \).
*
* Class is immutable.
*/
public final class LogGamma {
/** Lanczos constant. */
private static final double LANCZOS_G = 607d / 128d;
/** Performance. */
private static final double HALF_LOG_2_PI = 0.5 * Math.log(2.0 * Math.PI);
/** Private constructor. */
private LogGamma() {
// intentionally empty.
}
/**
* Computes the function \( \ln \Gamma(x) \) for {@code x >= 0}.
*
* For {@code x <= 8}, the implementation is based on the double precision
* implementation in the NSWC Library of Mathematics Subroutines,
* {@code DGAMLN}. For {@code x >= 8}, the implementation is based on
*
* - Gamma
* Function, equation (28).
* -
* Lanczos Approximation, equations (1) through (5).
* - Paul Godfrey, A note on
* the computation of the convergent Lanczos complex Gamma
* approximation
*
*
* @param x Argument.
* @return \( \ln \Gamma(x) \), or {@code NaN} if {@code x <= 0}.
*/
public static double value(double x) {
if (Double.isNaN(x) || (x <= 0.0)) {
return Double.NaN;
} else if (x < 0.5) {
return LogGamma1p.value(x) - Math.log(x);
} else if (x <= 2.5) {
return LogGamma1p.value((x - 0.5) - 0.5);
} else if (x <= 8.0) {
final int n = (int) Math.floor(x - 1.5);
double prod = 1.0;
for (int i = 1; i <= n; i++) {
prod *= x - i;
}
return LogGamma1p.value(x - (n + 1)) + Math.log(prod);
} else {
final double sum = LanczosApproximation.value(x);
final double tmp = x + LANCZOS_G + .5;
return ((x + .5) * Math.log(tmp)) - tmp +
HALF_LOG_2_PI + Math.log(sum / x);
}
}
}