Java tutorial
/* * 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.math3.random; import org.apache.commons.math3.exception.DimensionMismatchException; import org.apache.commons.math3.exception.NotPositiveException; import org.apache.commons.math3.exception.NullArgumentException; import org.apache.commons.math3.exception.OutOfRangeException; import org.apache.commons.math3.util.MathUtils; /** * Implementation of a Halton sequence. * <p> * A Halton sequence is a low-discrepancy sequence generating points in the interval [0, 1] according to * <pre> * H(n) = d_0 / b + d_1 / b^2 .... d_j / b^j+1 * * with * * n = d_j * b^j-1 + ... d_1 * b + d_0 * b^0 * </pre> * For higher dimensions, subsequent prime numbers are used as base, e.g. { 2, 3, 5 } for a Halton sequence in R^3. * <p> * Halton sequences are known to suffer from linear correlation for larger prime numbers, thus the individual digits * are usually scrambled. This implementation already comes with support for up to 40 dimensions with optimal weight * numbers from <a href="http://etd.lib.fsu.edu/theses/available/etd-07062004-140409/unrestricted/dissertation1.pdf"> * H. Chi: Scrambled quasirandom sequences and their applications</a>. * <p> * The generator supports two modes: * <ul> * <li>sequential generation of points: {@link #nextVector()}</li> * <li>random access to the i-th point in the sequence: {@link #skipTo(int)}</li> * </ul> * * @see <a href="http://en.wikipedia.org/wiki/Halton_sequence">Halton sequence (Wikipedia)</a> * @see <a href="https://lirias.kuleuven.be/bitstream/123456789/131168/1/mcm2005_bartv.pdf"> * On the Halton sequence and its scramblings</a> * @since 3.3 */ public class HaltonSequenceGenerator implements RandomVectorGenerator { /** The first 40 primes. */ private static final int[] PRIMES = new int[] { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173 }; /** The optimal weights used for scrambling of the first 40 dimension. */ private static final int[] WEIGHTS = new int[] { 1, 2, 3, 3, 8, 11, 12, 14, 7, 18, 12, 13, 17, 18, 29, 14, 18, 43, 41, 44, 40, 30, 47, 65, 71, 28, 40, 60, 79, 89, 56, 50, 52, 61, 108, 56, 66, 63, 60, 66 }; /** Space dimension. */ private final int dimension; /** The current index in the sequence. */ private int count = 0; /** The base numbers for each component. */ private final int[] base; /** The scrambling weights for each component. */ private final int[] weight; /** * Construct a new Halton sequence generator for the given space dimension. * * @param dimension the space dimension * @throws OutOfRangeException if the space dimension is outside the allowed range of [1, 40] */ public HaltonSequenceGenerator(final int dimension) throws OutOfRangeException { this(dimension, PRIMES, WEIGHTS); } /** * Construct a new Halton sequence generator with the given base numbers and weights for each dimension. * The length of the bases array defines the space dimension and is required to be > 0. * * @param dimension the space dimension * @param bases the base number for each dimension, entries should be (pairwise) prime, may not be null * @param weights the weights used during scrambling, may be null in which case no scrambling will be performed * @throws NullArgumentException if base is null * @throws OutOfRangeException if the space dimension is outside the range [1, len], where * len refers to the length of the bases array * @throws DimensionMismatchException if weights is non-null and the length of the input arrays differ */ public HaltonSequenceGenerator(final int dimension, final int[] bases, final int[] weights) throws NullArgumentException, OutOfRangeException, DimensionMismatchException { MathUtils.checkNotNull(bases); if (dimension < 1 || dimension > bases.length) { throw new OutOfRangeException(dimension, 1, PRIMES.length); } if (weights != null && weights.length != bases.length) { throw new DimensionMismatchException(weights.length, bases.length); } this.dimension = dimension; this.base = bases.clone(); this.weight = weights == null ? null : weights.clone(); count = 0; } /** {@inheritDoc} */ public double[] nextVector() { final double[] v = new double[dimension]; for (int i = 0; i < dimension; i++) { int index = count; double f = 1.0 / base[i]; int j = 0; while (index > 0) { final int digit = scramble(i, j, base[i], index % base[i]); v[i] += f * digit; index /= base[i]; // floor( index / base ) f /= base[i]; } } count++; return v; } /** * Performs scrambling of digit {@code d_j} according to the formula: * <pre> * ( weight_i * d_j ) mod base * </pre> * Implementations can override this method to do a different scrambling. * * @param i the dimension index * @param j the digit index * @param b the base for this dimension * @param digit the j-th digit * @return the scrambled digit */ protected int scramble(final int i, final int j, final int b, final int digit) { return weight != null ? (weight[i] * digit) % b : digit; } /** * Skip to the i-th point in the Halton sequence. * <p> * This operation can be performed in O(1). * * @param index the index in the sequence to skip to * @return the i-th point in the Halton sequence * @throws NotPositiveException if index < 0 */ public double[] skipTo(final int index) throws NotPositiveException { count = index; return nextVector(); } /** * Returns the index i of the next point in the Halton sequence that will be returned * by calling {@link #nextVector()}. * * @return the index of the next point */ public int getNextIndex() { return count; } }