Source code

001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017package org.apache.commons.math3.random;
018
019import java.io.BufferedReader;
020import java.io.IOException;
021import java.io.InputStream;
022import java.io.InputStreamReader;
023import java.nio.charset.Charset;
024import java.util.Arrays;
025import java.util.NoSuchElementException;
026import java.util.StringTokenizer;
027
028import org.apache.commons.math3.exception.MathInternalError;
029import org.apache.commons.math3.exception.MathParseException;
030import org.apache.commons.math3.exception.NotPositiveException;
031import org.apache.commons.math3.exception.NotStrictlyPositiveException;
032import org.apache.commons.math3.exception.OutOfRangeException;
033import org.apache.commons.math3.util.FastMath;
034
035/**
036 * Implementation of a Sobol sequence.
037 * <p>
038 * A Sobol sequence is a low-discrepancy sequence with the property that for all values of N,
039 * its subsequence (x1, ... xN) has a low discrepancy. It can be used to generate pseudo-random
040 * points in a space S, which are equi-distributed.
041 * <p>
042 * The implementation already comes with support for up to 1000 dimensions with direction numbers
043 * calculated from <a href="http://web.maths.unsw.edu.au/~fkuo/sobol/">Stephen Joe and Frances Kuo</a>.
044 * <p>
045 * The generator supports two modes:
046 * <ul>
047 *   <li>sequential generation of points: {@link #nextVector()}</li>
048 *   <li>random access to the i-th point in the sequence: {@link #skipTo(int)}</li>
049 * </ul>
050 *
051 * @see <a href="http://en.wikipedia.org/wiki/Sobol_sequence">Sobol sequence (Wikipedia)</a>
052 * @see <a href="http://web.maths.unsw.edu.au/~fkuo/sobol/">Sobol sequence direction numbers</a>
053 *
054 * @since 3.3
055 */
056public class SobolSequenceGenerator implements RandomVectorGenerator {
057
058    /** The number of bits to use. */
059    private static final int BITS = 52;
060
061    /** The scaling factor. */
062    private static final double SCALE = FastMath.pow(2, BITS);
063
064    /** The maximum supported space dimension. */
065    private static final int MAX_DIMENSION = 1000;
066
067    /** The resource containing the direction numbers. */
068    private static final String RESOURCE_NAME = "/assets/org/apache/commons/math3/random/new-joe-kuo-6.1000";
069
070    /** Character set for file input. */
071    private static final String FILE_CHARSET = "US-ASCII";
072
073    /** Space dimension. */
074    private final int dimension;
075
076    /** The current index in the sequence. */
077    private int count = 0;
078
079    /** The direction vector for each component. */
080    private final long[][] direction;
081
082    /** The current state. */
083    private final long[] x;
084
085    /**
086     * Construct a new Sobol sequence generator for the given space dimension.
087     *
088     * @param dimension the space dimension
089     * @throws OutOfRangeException if the space dimension is outside the allowed range of [1, 1000]
090     */
091    public SobolSequenceGenerator(final int dimension) throws OutOfRangeException {
092        if (dimension < 1 || dimension > MAX_DIMENSION) {
093            throw new OutOfRangeException(dimension, 1, MAX_DIMENSION);
094        }
095
096        // initialize the other dimensions with direction numbers from a resource
097        final InputStream is = getClass().getResourceAsStream(RESOURCE_NAME);
098        if (is == null) {
099            throw new MathInternalError();
100        }
101
102        this.dimension = dimension;
103
104        // init data structures
105        direction = new long[dimension][BITS + 1];
106        x = new long[dimension];
107
108        try {
109            initFromStream(is);
110        } catch (IOException e) {
111            // the internal resource file could not be read -> should not happen
112            throw new MathInternalError();
113        } catch (MathParseException e) {
114            // the internal resource file could not be parsed -> should not happen
115            throw new MathInternalError();
116        } finally {
117            try {
118                is.close();
119            } catch (IOException e) { // NOPMD
120                // ignore
121            }
122        }
123    }
124
125    /**
126     * Construct a new Sobol sequence generator for the given space dimension with
127     * direction vectors loaded from the given stream.
128     * <p>
129     * The expected format is identical to the files available from
130     * <a href="http://web.maths.unsw.edu.au/~fkuo/sobol/">Stephen Joe and Frances Kuo</a>.
131     * The first line will be ignored as it is assumed to contain only the column headers.
132     * The columns are:
133     * <ul>
134     *  <li>d: the dimension</li>
135     *  <li>s: the degree of the primitive polynomial</li>
136     *  <li>a: the number representing the coefficients</li>
137     *  <li>m: the list of initial direction numbers</li>
138     * </ul>
139     * Example:
140     * <pre>
141     * d       s       a       m_i
142     * 2       1       0       1
143     * 3       2       1       1 3
144     * </pre>
145     * <p>
146     * The input stream <i>must</i> be an ASCII text containing one valid direction vector per line.
147     *
148     * @param dimension the space dimension
149     * @param is the stream to read the direction vectors from
150     * @throws NotStrictlyPositiveException if the space dimension is &lt; 1
151     * @throws OutOfRangeException if the space dimension is outside the range [1, max], where
152     *   max refers to the maximum dimension found in the input stream
153     * @throws MathParseException if the content in the stream could not be parsed successfully
154     * @throws IOException if an error occurs while reading from the input stream
155     */
156    public SobolSequenceGenerator(final int dimension, final InputStream is)
157            throws NotStrictlyPositiveException, MathParseException, IOException {
158
159        if (dimension < 1) {
160            throw new NotStrictlyPositiveException(dimension);
161        }
162
163        this.dimension = dimension;
164
165        // init data structures
166        direction = new long[dimension][BITS + 1];
167        x = new long[dimension];
168
169        // initialize the other dimensions with direction numbers from the stream
170        int lastDimension = initFromStream(is);
171        if (lastDimension < dimension) {
172            throw new OutOfRangeException(dimension, 1, lastDimension);
173        }
174    }
175
176    /**
177     * Load the direction vector for each dimension from the given stream.
178     * <p>
179     * The input stream <i>must</i> be an ASCII text containing one
180     * valid direction vector per line.
181     *
182     * @param is the input stream to read the direction vector from
183     * @return the last dimension that has been read from the input stream
184     * @throws IOException if the stream could not be read
185     * @throws MathParseException if the content could not be parsed successfully
186     */
187    private int initFromStream(final InputStream is) throws MathParseException, IOException {
188
189        // special case: dimension 1 -> use unit initialization
190        for (int i = 1; i <= BITS; i++) {
191            direction[0][i] = 1l << (BITS - i);
192        }
193
194        final Charset charset = Charset.forName(FILE_CHARSET);
195        final BufferedReader reader = new BufferedReader(new InputStreamReader(is, charset));
196        int dim = -1;
197
198        try {
199            // ignore first line
200            reader.readLine();
201
202            int lineNumber = 2;
203            int index = 1;
204            String line = null;
205            while ( (line = reader.readLine()) != null) {
206                StringTokenizer st = new StringTokenizer(line, " ");
207                try {
208                    dim = Integer.parseInt(st.nextToken());
209                    if (dim >= 2 && dim <= dimension) { // we have found the right dimension
210                        final int s = Integer.parseInt(st.nextToken());
211                        final int a = Integer.parseInt(st.nextToken());
212                        final int[] m = new int[s + 1];
213                        for (int i = 1; i <= s; i++) {
214                            m[i] = Integer.parseInt(st.nextToken());
215                        }
216                        initDirectionVector(index++, a, m);
217                    }
218
219                    if (dim > dimension) {
220                        return dim;
221                    }
222                } catch (NoSuchElementException e) {
223                    throw new MathParseException(line, lineNumber);
224                } catch (NumberFormatException e) {
225                    throw new MathParseException(line, lineNumber);
226                }
227                lineNumber++;
228            }
229        } finally {
230            reader.close();
231        }
232
233        return dim;
234    }
235
236    /**
237     * Calculate the direction numbers from the given polynomial.
238     *
239     * @param d the dimension, zero-based
240     * @param a the coefficients of the primitive polynomial
241     * @param m the initial direction numbers
242     */
243    private void initDirectionVector(final int d, final int a, final int[] m) {
244        final int s = m.length - 1;
245        for (int i = 1; i <= s; i++) {
246            direction[d][i] = ((long) m[i]) << (BITS - i);
247        }
248        for (int i = s + 1; i <= BITS; i++) {
249            direction[d][i] = direction[d][i - s] ^ (direction[d][i - s] >> s);
250            for (int k = 1; k <= s - 1; k++) {
251                direction[d][i] ^= ((a >> (s - 1 - k)) & 1) * direction[d][i - k];
252            }
253        }
254    }
255
256    /** {@inheritDoc} */
257    public double[] nextVector() {
258        final double[] v = new double[dimension];
259        if (count == 0) {
260            count++;
261            return v;
262        }
263
264        // find the index c of the rightmost 0
265        int c = 1;
266        int value = count - 1;
267        while ((value & 1) == 1) {
268            value >>= 1;
269            c++;
270        }
271
272        for (int i = 0; i < dimension; i++) {
273            x[i] ^= direction[i][c];
274            v[i] = (double) x[i] / SCALE;
275        }
276        count++;
277        return v;
278    }
279
280    /**
281     * Skip to the i-th point in the Sobol sequence.
282     * <p>
283     * This operation can be performed in O(1).
284     *
285     * @param index the index in the sequence to skip to
286     * @return the i-th point in the Sobol sequence
287     * @throws NotPositiveException if index &lt; 0
288     */
289    public double[] skipTo(final int index) throws NotPositiveException {
290        if (index == 0) {
291            // reset x vector
292            Arrays.fill(x, 0);
293        } else {
294            final int i = index - 1;
295            final long grayCode = i ^ (i >> 1); // compute the gray code of i = i XOR floor(i / 2)
296            for (int j = 0; j < dimension; j++) {
297                long result = 0;
298                for (int k = 1; k <= BITS; k++) {
299                    final long shift = grayCode >> (k - 1);
300                    if (shift == 0) {
301                        // stop, as all remaining bits will be zero
302                        break;
303                    }
304                    // the k-th bit of i
305                    final long ik = shift & 1;
306                    result ^= ik * direction[j][k];
307                }
308                x[j] = result;
309            }
310        }
311        count = index;
312        return nextVector();
313    }
314
315    /**
316     * Returns the index i of the next point in the Sobol sequence that will be returned
317     * by calling {@link #nextVector()}.
318     *
319     * @return the index of the next point
320     */
321    public int getNextIndex() {
322        return count;
323    }
324
325}