cern.jet.random.tdouble.Gamma Maven / Gradle / Ivy
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/*
Copyright (C) 1999 CERN - European Organization for Nuclear Research.
Permission to use, copy, modify, distribute and sell this software and its documentation for any purpose
is hereby granted without fee, provided that the above copyright notice appear in all copies and
that both that copyright notice and this permission notice appear in supporting documentation.
CERN makes no representations about the suitability of this software for any purpose.
It is provided "as is" without expressed or implied warranty.
*/
package cern.jet.random.tdouble;
import cern.jet.random.tdouble.engine.DoubleRandomEngine;
import cern.jet.stat.tdouble.Probability;
/**
* Gamma distribution; math
* definition, definition of gamma function and
* animated definition.
*
* p(x) = k * x^(alpha-1) * e^(-x/beta) with
* k = 1/(g(alpha) * b^a)) and g(a) being the gamma function.
*
* Valid parameter ranges: alpha > 0.
*
* Note: For a Gamma distribution to have the mean mean and variance
* variance, set the parameters as follows:
*
*
* alpha = mean * mean / variance;
* lambda = 1 / (variance / mean);
*
*
*
* Instance methods operate on a user supplied uniform random number generator;
* they are unsynchronized.
*
Static methods operate on a default uniform random number generator; they
* are synchronized.
*
* Implementation:
*
Method: Acceptance Rejection combined with Acceptance Complement.
* High performance implementation. This is a port of RandGamma used in CLHEP
* 1.4.0 (C++). CLHEP's implementation, in turn, is based on gds.c
* from the C-RAND
* / WIN-RAND library. C-RAND's implementation, in turn, is based upon
*
* J.H. Ahrens, U. Dieter (1974): Computer methods for sampling from gamma,
* beta, Poisson and binomial distributions, Computing 12, 223-246.
*
* and
*
* J.H. Ahrens, U. Dieter (1982): Generating gamma variates by a modified
* rejection technique, Communications of the ACM 25, 47-54.
*
* @author [email protected]
* @version 1.0, 09/24/99
*/
public class Gamma extends AbstractContinousDoubleDistribution {
/**
*
*/
private static final long serialVersionUID = 1L;
protected double alpha;
protected double lambda;
// The uniform random number generated shared by all static methods.
protected static Gamma shared = new Gamma(1.0, 1.0, makeDefaultGenerator());
/**
* Constructs a Gamma distribution. Example: alpha=1.0, lambda=1.0.
*
* @throws IllegalArgumentException
* if alpha <= 0.0 || lambda <= 0.0.
*/
public Gamma(double alpha, double lambda, DoubleRandomEngine randomGenerator) {
setRandomGenerator(randomGenerator);
setState(alpha, lambda);
}
/**
* Returns the cumulative distribution function.
*/
public double cdf(double x) {
return Probability.gamma(alpha, lambda, x);
}
/**
* Returns a random number from the distribution.
*/
public double nextDouble() {
return nextDouble(alpha, lambda);
}
/**
* Returns a random number from the distribution; bypasses the internal
* state.
*/
public double nextDouble(double alpha, double lambda) {
/***********************************************************************
* * Gamma Distribution - Acceptance Rejection combined with *
* Acceptance Complement * *
* ***************************************************************** *
* FUNCTION: - gds samples a random number from the standard * gamma
* distribution with parameter a > 0. * Acceptance Rejection gs for a <
* 1 , * Acceptance Complement gd for a >= 1 . * REFERENCES: - J.H.
* Ahrens, U. Dieter (1974): Computer methods * for sampling from gamma,
* beta, Poisson and * binomial distributions, Computing 12, 223-246. *
* - J.H. Ahrens, U. Dieter (1982): Generating gamma * variates by a
* modified rejection technique, * Communications of the ACM 25, 47-54.
* * SUBPROGRAMS: - drand(seed) ... (0,1)-Uniform generator with *
* unsigned long integer *seed * - NORMAL(seed) ... Normal generator
* N(0,1). * *
**********************************************************************/
double a = alpha;
double aa = -1.0, aaa = -1.0, b = 0.0, c = 0.0, d = 0.0, e, r, s = 0.0, si = 0.0, ss = 0.0, q0 = 0.0, q1 = 0.0416666664, q2 = 0.0208333723, q3 = 0.0079849875, q4 = 0.0015746717, q5 = -0.0003349403, q6 = 0.0003340332, q7 = 0.0006053049, q8 = -0.0004701849, q9 = 0.0001710320, a1 = 0.333333333, a2 = -0.249999949, a3 = 0.199999867, a4 = -0.166677482, a5 = 0.142873973, a6 = -0.124385581, a7 = 0.110368310, a8 = -0.112750886, a9 = 0.104089866, e1 = 1.000000000, e2 = 0.499999994, e3 = 0.166666848, e4 = 0.041664508, e5 = 0.008345522, e6 = 0.001353826, e7 = 0.000247453;
double gds, p, q, t, sign_u, u, v, w, x;
double v1, v2, v12;
// Check for invalid input values
if (a <= 0.0)
throw new IllegalArgumentException();
if (lambda <= 0.0)
new IllegalArgumentException();
if (a < 1.0) { // CASE A: Acceptance rejection algorithm gs
b = 1.0 + 0.36788794412 * a; // Step 1
for (;;) {
p = b * randomGenerator.raw();
if (p <= 1.0) { // Step 2. Case gds <= 1
gds = Math.exp(Math.log(p) / a);
if (Math.log(randomGenerator.raw()) <= -gds)
return (gds / lambda);
} else { // Step 3. Case gds > 1
gds = -Math.log((b - p) / a);
if (Math.log(randomGenerator.raw()) <= ((a - 1.0) * Math.log(gds)))
return (gds / lambda);
}
}
}
else { // CASE B: Acceptance complement algorithm gd (gaussian
// distribution, box muller transformation)
if (a != aa) { // Step 1. Preparations
aa = a;
ss = a - 0.5;
s = Math.sqrt(ss);
d = 5.656854249 - 12.0 * s;
}
// Step 2. Normal deviate
do {
v1 = 2.0 * randomGenerator.raw() - 1.0;
v2 = 2.0 * randomGenerator.raw() - 1.0;
v12 = v1 * v1 + v2 * v2;
} while (v12 > 1.0);
t = v1 * Math.sqrt(-2.0 * Math.log(v12) / v12);
x = s + 0.5 * t;
gds = x * x;
if (t >= 0.0)
return (gds / lambda); // Immediate acceptance
u = randomGenerator.raw(); // Step 3. Uniform random number
if (d * u <= t * t * t)
return (gds / lambda); // Squeeze acceptance
if (a != aaa) { // Step 4. Set-up for hat case
aaa = a;
r = 1.0 / a;
q0 = ((((((((q9 * r + q8) * r + q7) * r + q6) * r + q5) * r + q4) * r + q3) * r + q2) * r + q1) * r;
if (a > 3.686) {
if (a > 13.022) {
b = 1.77;
si = 0.75;
c = 0.1515 / s;
} else {
b = 1.654 + 0.0076 * ss;
si = 1.68 / s + 0.275;
c = 0.062 / s + 0.024;
}
} else {
b = 0.463 + s - 0.178 * ss;
si = 1.235;
c = 0.195 / s - 0.079 + 0.016 * s;
}
}
if (x > 0.0) { // Step 5. Calculation of q
v = t / (s + s); // Step 6.
if (Math.abs(v) > 0.25) {
q = q0 - s * t + 0.25 * t * t + (ss + ss) * Math.log(1.0 + v);
} else {
q = q0
+ 0.5
* t
* t
* ((((((((a9 * v + a8) * v + a7) * v + a6) * v + a5) * v + a4) * v + a3) * v + a2) * v + a1)
* v;
} // Step 7. Quotient acceptance
if (Math.log(1.0 - u) <= q)
return (gds / lambda);
}
for (;;) { // Step 8. Double exponential deviate t
do {
e = -Math.log(randomGenerator.raw());
u = randomGenerator.raw();
u = u + u - 1.0;
sign_u = (u > 0) ? 1.0 : -1.0;
t = b + (e * si) * sign_u;
} while (t <= -0.71874483771719); // Step 9. Rejection of t
v = t / (s + s); // Step 10. New q(t)
if (Math.abs(v) > 0.25) {
q = q0 - s * t + 0.25 * t * t + (ss + ss) * Math.log(1.0 + v);
} else {
q = q0
+ 0.5
* t
* t
* ((((((((a9 * v + a8) * v + a7) * v + a6) * v + a5) * v + a4) * v + a3) * v + a2) * v + a1)
* v;
}
if (q <= 0.0)
continue; // Step 11.
if (q > 0.5) {
w = Math.exp(q) - 1.0;
} else {
w = ((((((e7 * q + e6) * q + e5) * q + e4) * q + e3) * q + e2) * q + e1) * q;
} // Step 12. Hat acceptance
if (c * u * sign_u <= w * Math.exp(e - 0.5 * t * t)) {
x = s + 0.5 * t;
return (x * x / lambda);
}
}
}
}
/**
* Returns the probability distribution function.
*/
public double pdf(double x) {
if (x < 0)
throw new IllegalArgumentException();
if (x == 0) {
if (alpha == 1.0)
return 1.0 / lambda;
else
return 0.0;
}
if (alpha == 1.0)
return Math.exp(-x / lambda) / lambda;
return Math.exp((alpha - 1.0) * Math.log(x / lambda) - x / lambda - Fun.logGamma(alpha)) / lambda;
}
/**
* Sets the mean and variance.
*
* @throws IllegalArgumentException
* if alpha <= 0.0 || lambda <= 0.0.
*/
public void setState(double alpha, double lambda) {
if (alpha <= 0.0)
throw new IllegalArgumentException();
if (lambda <= 0.0)
throw new IllegalArgumentException();
this.alpha = alpha;
this.lambda = lambda;
}
/**
* Returns a random number from the distribution.
*
* @throws IllegalArgumentException
* if alpha <= 0.0 || lambda <= 0.0.
*/
public static double staticNextDouble(double alpha, double lambda) {
synchronized (shared) {
return shared.nextDouble(alpha, lambda);
}
}
/**
* Returns a String representation of the receiver.
*/
public String toString() {
return this.getClass().getName() + "(" + alpha + "," + lambda + ")";
}
/**
* Sets the uniform random number generated shared by all static
* methods.
*
* @param randomGenerator
* the new uniform random number generator to be shared.
*/
private static void xstaticSetRandomGenerator(DoubleRandomEngine randomGenerator) {
synchronized (shared) {
shared.setRandomGenerator(randomGenerator);
}
}
}