/*
* 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 java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.nio.charset.Charset;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.StringTokenizer;
import org.apache.commons.math3.exception.MathInternalError;
import org.apache.commons.math3.exception.MathParseException;
import org.apache.commons.math3.exception.NotPositiveException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.util.FastMath;
/**
* Implementation of a Sobol sequence.
* <p>
* A Sobol sequence is a low-discrepancy sequence with the property that for all values of N,
* its subsequence (x1, ... xN) has a low discrepancy. It can be used to generate pseudo-random
* points in a space S, which are equi-distributed.
* <p>
* The implementation already comes with support for up to 1000 dimensions with direction numbers
* calculated from <a href="http://web.maths.unsw.edu.au/~fkuo/sobol/">Stephen Joe and Frances Kuo</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/Sobol_sequence">Sobol sequence (Wikipedia)</a>
* @see <a href="http://web.maths.unsw.edu.au/~fkuo/sobol/">Sobol sequence direction numbers</a>
*
* @since 3.3
*/
public class SobolSequenceGenerator implements RandomVectorGenerator {
/** The number of bits to use. */
private static final int BITS = 52;
/** The scaling factor. */
private static final double SCALE = FastMath.pow(2, BITS);
/** The maximum supported space dimension. */
private static final int MAX_DIMENSION = 1000;
/** The resource containing the direction numbers. */
private static final String RESOURCE_NAME = "/assets/org/apache/commons/math3/random/new-joe-kuo-6.1000";
/** Character set for file input. */
private static final String FILE_CHARSET = "US-ASCII";
/** Space dimension. */
private final int dimension;
/** The current index in the sequence. */
private int count = 0;
/** The direction vector for each component. */
private final long[][] direction;
/** The current state. */
private final long[] x;
/**
* Construct a new Sobol 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, 1000]
*/
public SobolSequenceGenerator(final int dimension) throws OutOfRangeException {
if (dimension < 1 || dimension > MAX_DIMENSION) {
throw new OutOfRangeException(dimension, 1, MAX_DIMENSION);
}
// initialize the other dimensions with direction numbers from a resource
final InputStream is = getClass().getResourceAsStream(RESOURCE_NAME);
if (is == null) {
throw new MathInternalError();
}
this.dimension = dimension;
// init data structures
direction = new long[dimension][BITS + 1];
x = new long[dimension];
try {
initFromStream(is);
} catch (IOException e) {
// the internal resource file could not be read -> should not happen
throw new MathInternalError();
} catch (MathParseException e) {
// the internal resource file could not be parsed -> should not happen
throw new MathInternalError();
} finally {
try {
is.close();
} catch (IOException e) { // NOPMD
// ignore
}
}
}
/**
* Construct a new Sobol sequence generator for the given space dimension with
* direction vectors loaded from the given stream.
* <p>
* The expected format is identical to the files available from
* <a href="http://web.maths.unsw.edu.au/~fkuo/sobol/">Stephen Joe and Frances Kuo</a>.
* The first line will be ignored as it is assumed to contain only the column headers.
* The columns are:
* <ul>
* <li>d: the dimension</li>
* <li>s: the degree of the primitive polynomial</li>
* <li>a: the number representing the coefficients</li>
* <li>m: the list of initial direction numbers</li>
* </ul>
* Example:
* <pre>
* d s a m_i
* 2 1 0 1
* 3 2 1 1 3
* </pre>
* <p>
* The input stream <i>must</i> be an ASCII text containing one valid direction vector per line.
*
* @param dimension the space dimension
* @param is the stream to read the direction vectors from
* @throws NotStrictlyPositiveException if the space dimension is < 1
* @throws OutOfRangeException if the space dimension is outside the range [1, max], where
* max refers to the maximum dimension found in the input stream
* @throws MathParseException if the content in the stream could not be parsed successfully
* @throws IOException if an error occurs while reading from the input stream
*/
public SobolSequenceGenerator(final int dimension, final InputStream is)
throws NotStrictlyPositiveException, MathParseException, IOException {
if (dimension < 1) {
throw new NotStrictlyPositiveException(dimension);
}
this.dimension = dimension;
// init data structures
direction = new long[dimension][BITS + 1];
x = new long[dimension];
// initialize the other dimensions with direction numbers from the stream
int lastDimension = initFromStream(is);
if (lastDimension < dimension) {
throw new OutOfRangeException(dimension, 1, lastDimension);
}
}
/**
* Load the direction vector for each dimension from the given stream.
* <p>
* The input stream <i>must</i> be an ASCII text containing one
* valid direction vector per line.
*
* @param is the input stream to read the direction vector from
* @return the last dimension that has been read from the input stream
* @throws IOException if the stream could not be read
* @throws MathParseException if the content could not be parsed successfully
*/
private int initFromStream(final InputStream is) throws MathParseException, IOException {
// special case: dimension 1 -> use unit initialization
for (int i = 1; i <= BITS; i++) {
direction[0][i] = 1l << (BITS - i);
}
final Charset charset = Charset.forName(FILE_CHARSET);
final BufferedReader reader = new BufferedReader(new InputStreamReader(is, charset));
int dim = -1;
try {
// ignore first line
reader.readLine();
int lineNumber = 2;
int index = 1;
String line = null;
while ( (line = reader.readLine()) != null) {
StringTokenizer st = new StringTokenizer(line, " ");
try {
dim = Integer.parseInt(st.nextToken());
if (dim >= 2 && dim <= dimension) { // we have found the right dimension
final int s = Integer.parseInt(st.nextToken());
final int a = Integer.parseInt(st.nextToken());
final int[] m = new int[s + 1];
for (int i = 1; i <= s; i++) {
m[i] = Integer.parseInt(st.nextToken());
}
initDirectionVector(index++, a, m);
}
if (dim > dimension) {
return dim;
}
} catch (NoSuchElementException e) {
throw new MathParseException(line, lineNumber);
} catch (NumberFormatException e) {
throw new MathParseException(line, lineNumber);
}
lineNumber++;
}
} finally {
reader.close();
}
return dim;
}
/**
* Calculate the direction numbers from the given polynomial.
*
* @param d the dimension, zero-based
* @param a the coefficients of the primitive polynomial
* @param m the initial direction numbers
*/
private void initDirectionVector(final int d, final int a, final int[] m) {
final int s = m.length - 1;
for (int i = 1; i <= s; i++) {
direction[d][i] = ((long) m[i]) << (BITS - i);
}
for (int i = s + 1; i <= BITS; i++) {
direction[d][i] = direction[d][i - s] ^ (direction[d][i - s] >> s);
for (int k = 1; k <= s - 1; k++) {
direction[d][i] ^= ((a >> (s - 1 - k)) & 1) * direction[d][i - k];
}
}
}
/** {@inheritDoc} */
public double[] nextVector() {
final double[] v = new double[dimension];
if (count == 0) {
count++;
return v;
}
// find the index c of the rightmost 0
int c = 1;
int value = count - 1;
while ((value & 1) == 1) {
value >>= 1;
c++;
}
for (int i = 0; i < dimension; i++) {
x[i] ^= direction[i][c];
v[i] = (double) x[i] / SCALE;
}
count++;
return v;
}
/**
* Skip to the i-th point in the Sobol 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 Sobol sequence
* @throws NotPositiveException if index < 0
*/
public double[] skipTo(final int index) throws NotPositiveException {
if (index == 0) {
// reset x vector
Arrays.fill(x, 0);
} else {
final int i = index - 1;
final long grayCode = i ^ (i >> 1); // compute the gray code of i = i XOR floor(i / 2)
for (int j = 0; j < dimension; j++) {
long result = 0;
for (int k = 1; k <= BITS; k++) {
final long shift = grayCode >> (k - 1);
if (shift == 0) {
// stop, as all remaining bits will be zero
break;
}
// the k-th bit of i
final long ik = shift & 1;
result ^= ik * direction[j][k];
}
x[j] = result;
}
}
count = index;
return nextVector();
}
/**
* Returns the index i of the next point in the Sobol sequence that will be returned
* by calling {@link #nextVector()}.
*
* @return the index of the next point
*/
public int getNextIndex() {
return count;
}
}