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| <div class="subTitle">org.apache.commons.math3.complex</div> |
| <h2 title="Class RootsOfUnity" class="title">Class RootsOfUnity</h2> |
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| <li>org.apache.commons.math3.complex.RootsOfUnity</li> |
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| <pre>public class <span class="strong">RootsOfUnity</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="http://docs.oracle.com/javase/6/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</a></pre> |
| <div class="block">A helper class for the computation and caching of the <code>n</code>-th roots of |
| unity.</div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>3.0</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: RootsOfUnity.java 1416643 2012-12-03 19:37:14Z tn $</dd> |
| <dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../serialized-form.html#org.apache.commons.math3.complex.RootsOfUnity">Serialized Form</a></dd></dl> |
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| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#RootsOfUnity()">RootsOfUnity</a></strong>()</code> |
| <div class="block">Build an engine for computing the <code>n</code>-th roots of unity.</div> |
| </td> |
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| <td class="colFirst"><code>void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#computeRoots(int)">computeRoots</a></strong>(int n)</code> |
| <div class="block"> |
| Computes the <code>n</code>-th roots of unity.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#getImaginary(int)">getImaginary</a></strong>(int k)</code> |
| <div class="block">Get the imaginary part of the <code>k</code>-th <code>n</code>-th root of unity.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>int</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#getNumberOfRoots()">getNumberOfRoots</a></strong>()</code> |
| <div class="block">Returns the number of roots of unity currently stored.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#getReal(int)">getReal</a></strong>(int k)</code> |
| <div class="block">Get the real part of the <code>k</code>-th <code>n</code>-th root of unity.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>boolean</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#isCounterClockWise()">isCounterClockWise</a></strong>()</code> |
| <div class="block">Returns <code>true</code> if <a href="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#computeRoots(int)"><code>computeRoots(int)</code></a> was called with a |
| positive value of its argument <code>n</code>.</div> |
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| <h4>RootsOfUnity</h4> |
| <pre>public RootsOfUnity()</pre> |
| <div class="block">Build an engine for computing the <code>n</code>-th roots of unity.</div> |
| </li> |
| </ul> |
| </li> |
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| <h4>isCounterClockWise</h4> |
| <pre>public boolean isCounterClockWise() |
| throws <a href="../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</a></pre> |
| <div class="block">Returns <code>true</code> if <a href="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#computeRoots(int)"><code>computeRoots(int)</code></a> was called with a |
| positive value of its argument <code>n</code>. If <code>true</code>, then |
| counter-clockwise ordering of the roots of unity should be used.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd><code>true</code> if the roots of unity are stored in |
| counter-clockwise order</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</a></code> - if no roots of unity have been computed |
| yet</dd></dl> |
| </li> |
| </ul> |
| <a name="computeRoots(int)"> |
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| <h4>computeRoots</h4> |
| <pre>public void computeRoots(int n) |
| throws <a href="../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</a></pre> |
| <div class="block"><p> |
| Computes the <code>n</code>-th roots of unity. The roots are stored in |
| <code>omega[]</code>, such that <code>omega[k] = w ^ k</code>, where |
| <code>k = 0, ..., n - 1</code>, <code>w = exp(2 * pi * i / n)</code> and |
| <code>i = sqrt(-1)</code>. |
| </p> |
| <p> |
| Note that <code>n</code> can be positive of negative |
| </p> |
| <ul> |
| <li><code>abs(n)</code> is always the number of roots of unity.</li> |
| <li>If <code>n > 0</code>, then the roots are stored in counter-clockwise order.</li> |
| <li>If <code>n < 0</code>, then the roots are stored in clockwise order.</p> |
| </ul></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>n</code> - the (signed) number of roots of unity to be computed</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</a></code> - if <code>n = 0</code></dd></dl> |
| </li> |
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| <h4>getReal</h4> |
| <pre>public double getReal(int k) |
| throws <a href="../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</a>, |
| <a href="../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></pre> |
| <div class="block">Get the real part of the <code>k</code>-th <code>n</code>-th root of unity.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>k</code> - index of the <code>n</code>-th root of unity</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>real part of the <code>k</code>-th <code>n</code>-th root of unity</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</a></code> - if no roots of unity have been |
| computed yet</dd> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if <code>k</code> is out of range</dd></dl> |
| </li> |
| </ul> |
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| <h4>getImaginary</h4> |
| <pre>public double getImaginary(int k) |
| throws <a href="../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</a>, |
| <a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></pre> |
| <div class="block">Get the imaginary part of the <code>k</code>-th <code>n</code>-th root of unity.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>k</code> - index of the <code>n</code>-th root of unity</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>imaginary part of the <code>k</code>-th <code>n</code>-th root of unity</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</a></code> - if no roots of unity have been |
| computed yet</dd> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></code> - if <code>k</code> is out of range</dd></dl> |
| </li> |
| </ul> |
| <a name="getNumberOfRoots()"> |
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| <h4>getNumberOfRoots</h4> |
| <pre>public int getNumberOfRoots()</pre> |
| <div class="block">Returns the number of roots of unity currently stored. If |
| <a href="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#computeRoots(int)"><code>computeRoots(int)</code></a> was called with <code>n</code>, then this method |
| returns <code>abs(n)</code>. If no roots of unity have been computed yet, this |
| method returns 0.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>the number of roots of unity currently stored</dd></dl> |
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