/**
* 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.hadoop.zebra.tfile;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Random;
/**
* A class that generates random numbers that follow some distribution.
*/
public class RandomDistribution {
/**
* Interface for discrete (integer) random distributions.
*/
public static interface DiscreteRNG {
/**
* Get the next random number
*
* @return the next random number.
*/
public int nextInt();
}
/**
* P(i)=1/(max-min)
*/
public static final class Flat implements DiscreteRNG {
private final Random random;
private final int min;
private final int max;
/**
* Generate random integers from min (inclusive) to max (exclusive)
* following even distribution.
*
* @param random
* The basic random number generator.
* @param min
* Minimum integer
* @param max
* maximum integer (exclusive).
*
*/
public Flat(Random random, int min, int max) {
if (min >= max) {
throw new IllegalArgumentException("Invalid range");
}
this.random = random;
this.min = min;
this.max = max;
}
/**
* @see DiscreteRNG#nextInt()
*/
@Override
public int nextInt() {
return random.nextInt(max - min) + min;
}
}
/**
* Zipf distribution. The ratio of the probabilities of integer i and j is
* defined as follows:
*
* P(i)/P(j)=((j-min+1)/(i-min+1))^sigma.
*/
public static final class Zipf implements DiscreteRNG {
private static final double DEFAULT_EPSILON = 0.001;
private final Random random;
private final ArrayList<Integer> k;
private final ArrayList<Double> v;
/**
* Constructor
*
* @param r
* The random number generator.
* @param min
* minimum integer (inclusvie)
* @param max
* maximum integer (exclusive)
* @param sigma
* parameter sigma. (sigma > 1.0)
*/
public Zipf(Random r, int min, int max, double sigma) {
this(r, min, max, sigma, DEFAULT_EPSILON);
}
/**
* Constructor.
*
* @param r
* The random number generator.
* @param min
* minimum integer (inclusvie)
* @param max
* maximum integer (exclusive)
* @param sigma
* parameter sigma. (sigma > 1.0)
* @param epsilon
* Allowable error percentage (0 < epsilon < 1.0).
*/
public Zipf(Random r, int min, int max, double sigma, double epsilon) {
if ((max <= min) || (sigma <= 1) || (epsilon <= 0)
|| (epsilon >= 0.5)) {
throw new IllegalArgumentException("Invalid arguments");
}
random = r;
k = new ArrayList<Integer>();
v = new ArrayList<Double>();
double sum = 0;
int last = -1;
for (int i = min; i < max; ++i) {
sum += Math.exp(-sigma * Math.log(i - min + 1));
if ((last == -1) || i * (1 - epsilon) > last) {
k.add(i);
v.add(sum);
last = i;
}
}
if (last != max - 1) {
k.add(max - 1);
v.add(sum);
}
v.set(v.size() - 1, 1.0);
for (int i = v.size() - 2; i >= 0; --i) {
v.set(i, v.get(i) / sum);
}
}
/**
* @see DiscreteRNG#nextInt()
*/
@Override
public int nextInt() {
double d = random.nextDouble();
int idx = Collections.binarySearch(v, d);
if (idx > 0) {
++idx;
}
else {
idx = -(idx + 1);
}
if (idx >= v.size()) {
idx = v.size() - 1;
}
if (idx == 0) {
return k.get(0);
}
int ceiling = k.get(idx);
int lower = k.get(idx - 1);
return ceiling - random.nextInt(ceiling - lower);
}
}
/**
* Binomial distribution.
*
* P(k)=select(n, k)*p^k*(1-p)^(n-k) (k = 0, 1, ..., n)
*
* P(k)=select(max-min-1, k-min)*p^(k-min)*(1-p)^(k-min)*(1-p)^(max-k-1)
*/
public static final class Binomial implements DiscreteRNG {
private final Random random;
private final int min;
private final int n;
private final double[] v;
private static double select(int n, int k) {
double ret = 1.0;
for (int i = k + 1; i <= n; ++i) {
ret *= (double) i / (i - k);
}
return ret;
}
private static double power(double p, int k) {
return Math.exp(k * Math.log(p));
}
/**
* Generate random integers from min (inclusive) to max (exclusive)
* following Binomial distribution.
*
* @param random
* The basic random number generator.
* @param min
* Minimum integer
* @param max
* maximum integer (exclusive).
* @param p
* parameter.
*
*/
public Binomial(Random random, int min, int max, double p) {
if (min >= max) {
throw new IllegalArgumentException("Invalid range");
}
this.random = random;
this.min = min;
this.n = max - min - 1;
if (n > 0) {
v = new double[n + 1];
double sum = 0.0;
for (int i = 0; i <= n; ++i) {
sum += select(n, i) * power(p, i) * power(1 - p, n - i);
v[i] = sum;
}
for (int i = 0; i <= n; ++i) {
v[i] /= sum;
}
}
else {
v = null;
}
}
/**
* @see DiscreteRNG#nextInt()
*/
@Override
public int nextInt() {
if (v == null) {
return min;
}
double d = random.nextDouble();
int idx = Arrays.binarySearch(v, d);
if (idx > 0) {
++idx;
} else {
idx = -(idx + 1);
}
if (idx >= v.length) {
idx = v.length - 1;
}
return idx + min;
}
}
}