/* * MersenneTwisterFast.java * * Copyright (C) 2002-2006 Alexei Drummond and Andrew Rambaut * * This file is part of BEAST. * See the NOTICE file distributed with this work for additional * information regarding copyright ownership and licensing. * * BEAST is free software; you can redistribute it and/or modify * it under the terms of the GNU Lesser General Public License as * published by the Free Software Foundation; either version 2 * of the License, or (at your option) any later version. * * BEAST is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU Lesser General Public License for more details. * * You should have received a copy of the GNU Lesser General Public * License along with BEAST; if not, write to the * Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, * Boston, MA 02110-1301 USA */ package math; import java.io.Serializable; /** * MersenneTwisterFast: * <p/> * A simulation quality fast random number generator (MT19937) with the same * public methods as java.util.Random. * <p/> * <p> * About the Mersenne Twister. This is a Java version of the C-program for * MT19937: Integer version. next(32) generates one pseudorandom unsigned * integer (32bit) which is uniformly distributed among 0 to 2^32-1 for each * call. next(int bits) >>>'s by (32-bits) to get a value ranging between 0 and * 2^bits-1 long inclusive; hope that's correct. setSeed(seed) set initial * values to the working area of 624 words. For setSeed(seed), seed is any * 32-bit integer except for 0. * <p/> * Reference. M. Matsumoto and T. Nishimura, "Mersenne Twister: A * 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator", * <i>ACM Transactions on Modeling and Computer Simulation,</i> Vol. 8, No. 1, * January 1998, pp 3--30. * <p/> * <p> * Bug Fixes. This implementation implements the bug fixes made in Java 1.2's * version of Random, which means it can be used with earlier versions of Java. * See <a href= * "http://www.javasoft.com/products/jdk/1.2/docs/api/java/util/Random.html"> * the JDK 1.2 java.util.Random documentation</a> for further documentation on * the random-number generation contracts made. Additionally, there's an * undocumented bug in the JDK java.util.Random.nextBytes() method, which this * code fixes. * <p/> * <p> * Important Note. Just like java.util.Random, this generator accepts a long * seed but doesn't use all of it. java.util.Random uses 48 bits. The Mersenne * Twister instead uses 32 bits (int size). So it's best if your seed does not * exceed the int range. * <p/> * <p> * <a href="http://www.cs.umd.edu/users/seanl/">Sean Luke's web page</a> * <p/> * <p/> * - added shuffling method (Alexei Drummond) * <p/> * - added gamma RV method (Marc Suchard) * <p/> * This is now package private - it should be accessed using the instance in * Random */ class MersenneTwisterFast implements Serializable { /** * */ private static final long serialVersionUID = 6185086957226269797L; // Period parameters private static final int N = 624; private static final int M = 397; private static final int MATRIX_A = 0x9908b0df; // private static final * // constant vector a private static final int UPPER_MASK = 0x80000000; // most significant w-r // bits private static final int LOWER_MASK = 0x7fffffff; // least significant r // bits // Tempering parameters private static final int TEMPERING_MASK_B = 0x9d2c5680; private static final int TEMPERING_MASK_C = 0xefc60000; // #define TEMPERING_SHIFT_U(y) (y >>> 11) // #define TEMPERING_SHIFT_S(y) (y << 7) // #define TEMPERING_SHIFT_T(y) (y << 15) // #define TEMPERING_SHIFT_L(y) (y >>> 18) private int mt[]; // the array for the state vector private int mti; // mti==N+1 means mt[N] is not initialized private int mag01[]; // a good initial seed (of int size, though stored in a long) private static final long GOOD_SEED = 4357; private double nextNextGaussian; private boolean haveNextNextGaussian; // The following can be accessed externally by the static accessor methods // which // inforce synchronization public static final MersenneTwisterFast DEFAULT_INSTANCE = new MersenneTwisterFast(); // Added to curernt time in default constructor, and then adjust to allow // for programs that construct // multiple MersenneTwisterFast in a short amount of time. private static long seedAdditive_ = 0; private long initializationSeed; /** * Constructor using the time of day as default seed. */ public MersenneTwisterFast() { this(System.currentTimeMillis() + seedAdditive_); seedAdditive_ += nextInt(); } /** * Constructor using a given seed. Though you pass this seed in as a long, * it's best to make sure it's actually an integer. * * @param seed * generator starting number, often the time of day. */ private MersenneTwisterFast(long seed) { if (seed == 0) { setSeed(GOOD_SEED); } else { setSeed(seed); } } /** * Initalize the pseudo random number generator. The Mersenne Twister only * uses an integer for its seed; It's best that you don't pass in a long * that's bigger than an int. * * @param seed * from constructor */ public final void setSeed(long seed) { if (seed == 0) { throw new IllegalArgumentException("Non zero random seed required."); } initializationSeed = seed; haveNextNextGaussian = false; mt = new int[N]; // setting initial seeds to mt[N] using // the generator Line 25 of Table 1 in // [KNUTH 1981, The Art of Computer Programming // Vol. 2 (2nd Ed.), pp102] // the 0xffffffff is commented out because in Java // ints are always 32 bits; hence i & 0xffffffff == i mt[0] = ((int) seed); // & 0xffffffff; for (mti = 1; mti < N; mti++) mt[mti] = (69069 * mt[mti - 1]); // & 0xffffffff; // mag01[x] = x * MATRIX_A for x=0,1 mag01 = new int[2]; mag01[0] = 0x0; mag01[1] = MATRIX_A; } public final long getSeed() { return initializationSeed; } public final int nextInt() { int y; if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1]; } for (; kk < N - 1; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1]; } y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1]; mti = 0; } y = mt[mti++]; y ^= y >>> 11; // TEMPERING_SHIFT_U(y) y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y) y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y) y ^= (y >>> 18); // TEMPERING_SHIFT_L(y) return y; } public final short nextShort() { int y; if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1]; } for (; kk < N - 1; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1]; } y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1]; mti = 0; } y = mt[mti++]; y ^= y >>> 11; // TEMPERING_SHIFT_U(y) y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y) y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y) y ^= (y >>> 18); // TEMPERING_SHIFT_L(y) return (short) (y >>> 16); } public final char nextChar() { int y; if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1]; } for (; kk < N - 1; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1]; } y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1]; mti = 0; } y = mt[mti++]; y ^= y >>> 11; // TEMPERING_SHIFT_U(y) y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y) y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y) y ^= (y >>> 18); // TEMPERING_SHIFT_L(y) return (char) (y >>> 16); } public final boolean nextBoolean() { int y; if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1]; } for (; kk < N - 1; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1]; } y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1]; mti = 0; } y = mt[mti++]; y ^= y >>> 11; // TEMPERING_SHIFT_U(y) y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y) y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y) y ^= (y >>> 18); // TEMPERING_SHIFT_L(y) return ((y >>> 31) != 0); } public final byte nextByte() { int y; if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1]; } for (; kk < N - 1; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1]; } y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1]; mti = 0; } y = mt[mti++]; y ^= y >>> 11; // TEMPERING_SHIFT_U(y) y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y) y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y) y ^= (y >>> 18); // TEMPERING_SHIFT_L(y) return (byte) (y >>> 24); } public final void nextBytes(byte[] bytes) { int y; for (int x = 0; x < bytes.length; x++) { if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1]; } for (; kk < N - 1; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1]; } y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1]; mti = 0; } y = mt[mti++]; y ^= y >>> 11; // TEMPERING_SHIFT_U(y) y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y) y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y) y ^= (y >>> 18); // TEMPERING_SHIFT_L(y) bytes[x] = (byte) (y >>> 24); } } public final long nextLong() { int y; int z; if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1]; } for (; kk < N - 1; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1]; } y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1]; mti = 0; } y = mt[mti++]; y ^= y >>> 11; // TEMPERING_SHIFT_U(y) y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y) y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y) y ^= (y >>> 18); // TEMPERING_SHIFT_L(y) if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { z = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (z >>> 1) ^ mag01[z & 0x1]; } for (; kk < N - 1; kk++) { z = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (z >>> 1) ^ mag01[z & 0x1]; } z = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (z >>> 1) ^ mag01[z & 0x1]; mti = 0; } z = mt[mti++]; z ^= z >>> 11; // TEMPERING_SHIFT_U(z) z ^= (z << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(z) z ^= (z << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(z) z ^= (z >>> 18); // TEMPERING_SHIFT_L(z) return (((long) y) << 32) + (long) z; } public final double nextDouble() { int y; int z; if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1]; } for (; kk < N - 1; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1]; } y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1]; mti = 0; } y = mt[mti++]; y ^= y >>> 11; // TEMPERING_SHIFT_U(y) y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y) y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y) y ^= (y >>> 18); // TEMPERING_SHIFT_L(y) if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { z = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (z >>> 1) ^ mag01[z & 0x1]; } for (; kk < N - 1; kk++) { z = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (z >>> 1) ^ mag01[z & 0x1]; } z = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (z >>> 1) ^ mag01[z & 0x1]; mti = 0; } z = mt[mti++]; z ^= z >>> 11; // TEMPERING_SHIFT_U(z) z ^= (z << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(z) z ^= (z << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(z) z ^= (z >>> 18); // TEMPERING_SHIFT_L(z) /* derived from nextDouble documentation in jdk 1.2 docs, see top */ return ((((long) (y >>> 6)) << 27) + (z >>> 5)) / (double) (1L << 53); } public final double nextGaussian() { if (haveNextNextGaussian) { haveNextNextGaussian = false; return nextNextGaussian; } else { double v1, v2, s; do { int y; int z; int a; int b; if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1]; } for (; kk < N - 1; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1]; } y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1]; mti = 0; } y = mt[mti++]; y ^= y >>> 11; // TEMPERING_SHIFT_U(y) y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y) y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y) y ^= (y >>> 18); // TEMPERING_SHIFT_L(y) if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { z = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (z >>> 1) ^ mag01[z & 0x1]; } for (; kk < N - 1; kk++) { z = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (z >>> 1) ^ mag01[z & 0x1]; } z = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (z >>> 1) ^ mag01[z & 0x1]; mti = 0; } z = mt[mti++]; z ^= z >>> 11; // TEMPERING_SHIFT_U(z) z ^= (z << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(z) z ^= (z << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(z) z ^= (z >>> 18); // TEMPERING_SHIFT_L(z) if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { a = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (a >>> 1) ^ mag01[a & 0x1]; } for (; kk < N - 1; kk++) { a = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (a >>> 1) ^ mag01[a & 0x1]; } a = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (a >>> 1) ^ mag01[a & 0x1]; mti = 0; } a = mt[mti++]; a ^= a >>> 11; // TEMPERING_SHIFT_U(a) a ^= (a << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(a) a ^= (a << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(a) a ^= (a >>> 18); // TEMPERING_SHIFT_L(a) if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { b = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (b >>> 1) ^ mag01[b & 0x1]; } for (; kk < N - 1; kk++) { b = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (b >>> 1) ^ mag01[b & 0x1]; } b = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (b >>> 1) ^ mag01[b & 0x1]; mti = 0; } b = mt[mti++]; b ^= b >>> 11; // TEMPERING_SHIFT_U(b) b ^= (b << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(b) b ^= (b << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(b) b ^= (b >>> 18); // TEMPERING_SHIFT_L(b) /* * derived from nextDouble documentation in jdk 1.2 docs, see * top */ v1 = 2 * (((((long) (y >>> 6)) << 27) + (z >>> 5)) / (double) (1L << 53)) - 1; v2 = 2 * (((((long) (a >>> 6)) << 27) + (b >>> 5)) / (double) (1L << 53)) - 1; s = v1 * v1 + v2 * v2; } while (s >= 1); double multiplier = Math.sqrt(-2 * Math.log(s) / s); nextNextGaussian = v2 * multiplier; haveNextNextGaussian = true; return v1 * multiplier; } } public final float nextFloat() { int y; if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1]; } for (; kk < N - 1; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1]; } y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1]; mti = 0; } y = mt[mti++]; y ^= y >>> 11; // TEMPERING_SHIFT_U(y) y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y) y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y) y ^= (y >>> 18); // TEMPERING_SHIFT_L(y) return (y >>> 8) / ((float) (1 << 24)); } /** * Returns an integer drawn uniformly from 0 to n-1. Suffice it to say, n * must be > 0, or an IllegalArgumentException is raised. */ public int nextInt(int n) { if (n <= 0) throw new IllegalArgumentException("n must be positive"); if ((n & -n) == n) // i.e., n is a power of 2 { int y; if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1]; } for (; kk < N - 1; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1]; } y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1]; mti = 0; } y = mt[mti++]; y ^= y >>> 11; // TEMPERING_SHIFT_U(y) y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y) y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y) y ^= (y >>> 18); // TEMPERING_SHIFT_L(y) return (int) ((n * (long) (y >>> 1)) >> 31); } int bits, val; do { int y; if (mti >= N) // generate N words at one time { int kk; for (kk = 0; kk < N - M; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + M] ^ (y >>> 1) ^ mag01[y & 0x1]; } for (; kk < N - 1; kk++) { y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK); mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ mag01[y & 0x1]; } y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK); mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ mag01[y & 0x1]; mti = 0; } y = mt[mti++]; y ^= y >>> 11; // TEMPERING_SHIFT_U(y) y ^= (y << 7) & TEMPERING_MASK_B; // TEMPERING_SHIFT_S(y) y ^= (y << 15) & TEMPERING_MASK_C; // TEMPERING_SHIFT_T(y) y ^= (y >>> 18); // TEMPERING_SHIFT_L(y) bits = (y >>> 1); val = bits % n; } while (bits - val + (n - 1) < 0); return val; } /** * Returns a uniform random permutation of int objects in array */ public final void permute(int[] array) { int l = array.length; for (int i = 0; i < l; i++) { int index = nextInt(l - i) + i; int temp = array[index]; array[index] = array[i]; array[i] = temp; } } /** * Shuffles an array. */ public final void shuffle(int[] array) { int l = array.length; for (int i = 0; i < l; i++) { int index = nextInt(l - i) + i; int temp = array[index]; array[index] = array[i]; array[i] = temp; } } /** * Shuffles an array. Shuffles numberOfShuffles times */ public final void shuffle(int[] array, int numberOfShuffles) { int i, j, temp, l = array.length; for (int shuffle = 0; shuffle < numberOfShuffles; shuffle++) { do { i = nextInt(l); j = nextInt(l); } while (i != j); temp = array[j]; array[j] = array[i]; array[i] = temp; } } /** * Returns an array of shuffled indices of length l. * * @param l * length of the array required. */ public int[] shuffled(int l) { int[] array = new int[l]; // initialize array for (int i = 0; i < l; i++) { array[i] = i; } shuffle(array); return array; } /** * Returns a uniform random permutation of ints 0,...,l-1 * * @param l * length of the array required. */ public int[] permuted(int l) { int[] array = new int[l]; // initialize array for (int i = 0; i < l; i++) { array[i] = i; } permute(array); return array; } public double nextGamma(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 * nextDouble(); if (p <= 1.0) { // Step 2. Case gds <= 1 gds = Math.exp(Math.log(p) / a); if (Math.log(nextDouble()) <= -gds) return (gds / lambda); } else { // Step 3. Case gds > 1 gds = -Math.log((b - p) / a); if (Math.log(nextDouble()) <= ((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 * nextDouble() - 1.0; v2 = 2.0 * nextDouble() - 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 = nextDouble(); // 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(nextDouble()); u = nextDouble(); 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); } } } } }