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| <h2 title="Class HaltonSequenceGenerator" class="title">Class HaltonSequenceGenerator</h2> |
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| <dt>All Implemented Interfaces:</dt> |
| <dd><a href="../../../../../org/apache/commons/math3/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math3.random">RandomVectorGenerator</a></dd> |
| </dl> |
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| <br> |
| <pre>public class <span class="strong">HaltonSequenceGenerator</span> |
| extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a> |
| implements <a href="../../../../../org/apache/commons/math3/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math3.random">RandomVectorGenerator</a></pre> |
| <div class="block">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: <a href="../../../../../org/apache/commons/math3/random/HaltonSequenceGenerator.html#nextVector()"><code>nextVector()</code></a></li> |
| <li>random access to the i-th point in the sequence: <a href="../../../../../org/apache/commons/math3/random/HaltonSequenceGenerator.html#skipTo(int)"><code>skipTo(int)</code></a></li> |
| </ul></div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>3.3</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: HaltonSequenceGenerator.java 1512043 2013-08-08 21:27:57Z tn $</dd> |
| <dt><span class="strong">See Also:</span></dt><dd><a href="http://en.wikipedia.org/wiki/Halton_sequence">Halton sequence (Wikipedia)</a>, |
| <a href="https://lirias.kuleuven.be/bitstream/123456789/131168/1/mcm2005_bartv.pdf"> |
| On the Halton sequence and its scramblings</a></dd></dl> |
| </li> |
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| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/random/HaltonSequenceGenerator.html#HaltonSequenceGenerator(int)">HaltonSequenceGenerator</a></strong>(int dimension)</code> |
| <div class="block">Construct a new Halton sequence generator for the given space dimension.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/random/HaltonSequenceGenerator.html#HaltonSequenceGenerator(int, int[], int[])">HaltonSequenceGenerator</a></strong>(int dimension, |
| int[] bases, |
| int[] weights)</code> |
| <div class="block">Construct a new Halton sequence generator with the given base numbers and weights for each dimension.</div> |
| </td> |
| </tr> |
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| <td class="colFirst"><code>int</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/random/HaltonSequenceGenerator.html#getNextIndex()">getNextIndex</a></strong>()</code> |
| <div class="block">Returns the index i of the next point in the Halton sequence that will be returned |
| by calling <a href="../../../../../org/apache/commons/math3/random/HaltonSequenceGenerator.html#nextVector()"><code>nextVector()</code></a>.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>double[]</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/random/HaltonSequenceGenerator.html#nextVector()">nextVector</a></strong>()</code> |
| <div class="block">Generate a random vector.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>protected int</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/random/HaltonSequenceGenerator.html#scramble(int, int, int, int)">scramble</a></strong>(int i, |
| int j, |
| int b, |
| int digit)</code> |
| <div class="block">Performs scrambling of digit <code>d_j</code> according to the formula:</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>double[]</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/random/HaltonSequenceGenerator.html#skipTo(int)">skipTo</a></strong>(int index)</code> |
| <div class="block">Skip to the i-th point in the Halton sequence.</div> |
| </td> |
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| <h4>HaltonSequenceGenerator</h4> |
| <pre>public HaltonSequenceGenerator(int dimension) |
| throws <a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></pre> |
| <div class="block">Construct a new Halton sequence generator for the given space dimension.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>dimension</code> - the space dimension</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></code> - if the space dimension is outside the allowed range of [1, 40]</dd></dl> |
| </li> |
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| <!-- --> |
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| <h4>HaltonSequenceGenerator</h4> |
| <pre>public HaltonSequenceGenerator(int dimension, |
| int[] bases, |
| int[] weights) |
| throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, |
| <a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a>, |
| <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></pre> |
| <div class="block">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.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>dimension</code> - the space dimension</dd><dd><code>bases</code> - the base number for each dimension, entries should be (pairwise) prime, may not be null</dd><dd><code>weights</code> - the weights used during scrambling, may be null in which case no scrambling will be performed</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if base is null</dd> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></code> - if the space dimension is outside the range [1, len], where |
| len refers to the length of the bases array</dd> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if weights is non-null and the length of the input arrays differ</dd></dl> |
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| <a name="nextVector()"> |
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| <h4>nextVector</h4> |
| <pre>public double[] nextVector()</pre> |
| <div class="block">Generate a random vector.</div> |
| <dl> |
| <dt><strong>Specified by:</strong></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/random/RandomVectorGenerator.html#nextVector()">nextVector</a></code> in interface <code><a href="../../../../../org/apache/commons/math3/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math3.random">RandomVectorGenerator</a></code></dd> |
| <dt><span class="strong">Returns:</span></dt><dd>a random vector as an array of double.</dd></dl> |
| </li> |
| </ul> |
| <a name="scramble(int, int, int, int)"> |
| <!-- --> |
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| <h4>scramble</h4> |
| <pre>protected int scramble(int i, |
| int j, |
| int b, |
| int digit)</pre> |
| <div class="block">Performs scrambling of digit <code>d_j</code> according to the formula: |
| <pre> |
| ( weight_i * d_j ) mod base |
| </pre> |
| Implementations can override this method to do a different scrambling.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>i</code> - the dimension index</dd><dd><code>j</code> - the digit index</dd><dd><code>b</code> - the base for this dimension</dd><dd><code>digit</code> - the j-th digit</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the scrambled digit</dd></dl> |
| </li> |
| </ul> |
| <a name="skipTo(int)"> |
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| <pre>public double[] skipTo(int index) |
| throws <a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></pre> |
| <div class="block">Skip to the i-th point in the Halton sequence. |
| <p> |
| This operation can be performed in O(1).</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>index</code> - the index in the sequence to skip to</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the i-th point in the Halton sequence</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if index < 0</dd></dl> |
| </li> |
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| <h4>getNextIndex</h4> |
| <pre>public int getNextIndex()</pre> |
| <div class="block">Returns the index i of the next point in the Halton sequence that will be returned |
| by calling <a href="../../../../../org/apache/commons/math3/random/HaltonSequenceGenerator.html#nextVector()"><code>nextVector()</code></a>.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>the index of the next point</dd></dl> |
| </li> |
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