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Diffstat (limited to 'src/main/java/org/apache/commons/math3/random/HaltonSequenceGenerator.java')
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diff --git a/src/main/java/org/apache/commons/math3/random/HaltonSequenceGenerator.java b/src/main/java/org/apache/commons/math3/random/HaltonSequenceGenerator.java new file mode 100644 index 0000000..2b1c623 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/random/HaltonSequenceGenerator.java @@ -0,0 +1,195 @@ +/* + * 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>random access to the i-th point in the sequence: {@link #skipTo(int)} + * </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; + } +} |