1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<!-- NewPage -->
<html lang="en">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>RootsOfUnity (Apache Commons Math 3.6.1 API)</title>
<link rel="stylesheet" type="text/css" href="../../../../../stylesheet.css" title="Style">
</head>
<body>
<script type="text/javascript"><!--
if (location.href.indexOf('is-external=true') == -1) {
parent.document.title="RootsOfUnity (Apache Commons Math 3.6.1 API)";
}
//-->
</script>
<noscript>
<div>JavaScript is disabled on your browser.</div>
</noscript>
<!-- ========= START OF TOP NAVBAR ======= -->
<div class="topNav"><a name="navbar_top">
<!-- -->
</a><a href="#skip-navbar_top" title="Skip navigation links"></a><a name="navbar_top_firstrow">
<!-- -->
</a>
<ul class="navList" title="Navigation">
<li><a href="../../../../../overview-summary.html">Overview</a></li>
<li><a href="package-summary.html">Package</a></li>
<li class="navBarCell1Rev">Class</li>
<li><a href="class-use/RootsOfUnity.html">Use</a></li>
<li><a href="package-tree.html">Tree</a></li>
<li><a href="../../../../../deprecated-list.html">Deprecated</a></li>
<li><a href="../../../../../index-all.html">Index</a></li>
<li><a href="../../../../../help-doc.html">Help</a></li>
</ul>
<div class="aboutLanguage"><em><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script></em></div>
</div>
<div class="subNav">
<ul class="navList">
<li><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex"><span class="strong">Prev Class</span></a></li>
<li>Next Class</li>
</ul>
<ul class="navList">
<li><a href="../../../../../index.html?org/apache/commons/math3/complex/RootsOfUnity.html" target="_top">Frames</a></li>
<li><a href="RootsOfUnity.html" target="_top">No Frames</a></li>
</ul>
<ul class="navList" id="allclasses_navbar_top">
<li><a href="../../../../../allclasses-noframe.html">All Classes</a></li>
</ul>
<div>
<script type="text/javascript"><!--
allClassesLink = document.getElementById("allclasses_navbar_top");
if(window==top) {
allClassesLink.style.display = "block";
}
else {
allClassesLink.style.display = "none";
}
//-->
</script>
</div>
<div>
<ul class="subNavList">
<li>Summary: </li>
<li>Nested | </li>
<li>Field | </li>
<li><a href="#constructor_summary">Constr</a> | </li>
<li><a href="#method_summary">Method</a></li>
</ul>
<ul class="subNavList">
<li>Detail: </li>
<li>Field | </li>
<li><a href="#constructor_detail">Constr</a> | </li>
<li><a href="#method_detail">Method</a></li>
</ul>
</div>
<a name="skip-navbar_top">
<!-- -->
</a></div>
<!-- ========= END OF TOP NAVBAR ========= -->
<!-- ======== START OF CLASS DATA ======== -->
<div class="header">
<div class="subTitle">org.apache.commons.math3.complex</div>
<h2 title="Class RootsOfUnity" class="title">Class RootsOfUnity</h2>
</div>
<div class="contentContainer">
<ul class="inheritance">
<li><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</a></li>
<li>
<ul class="inheritance">
<li>org.apache.commons.math3.complex.RootsOfUnity</li>
</ul>
</li>
</ul>
<div class="description">
<ul class="blockList">
<li class="blockList">
<dl>
<dt>All Implemented Interfaces:</dt>
<dd><a href="http://docs.oracle.com/javase/7/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</a></dd>
</dl>
<hr>
<br>
<pre>public class <span class="strong">RootsOfUnity</span>
extends <a href="http://docs.oracle.com/javase/7/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/7/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">See Also:</span></dt><dd><a href="../../../../../serialized-form.html#org.apache.commons.math3.complex.RootsOfUnity">Serialized Form</a></dd></dl>
</li>
</ul>
</div>
<div class="summary">
<ul class="blockList">
<li class="blockList">
<!-- ======== CONSTRUCTOR SUMMARY ======== -->
<ul class="blockList">
<li class="blockList"><a name="constructor_summary">
<!-- -->
</a>
<h3>Constructor Summary</h3>
<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Constructor Summary table, listing constructors, and an explanation">
<caption><span>Constructors</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colOne" scope="col">Constructor and Description</th>
</tr>
<tr class="altColor">
<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>
</tr>
</table>
</li>
</ul>
<!-- ========== METHOD SUMMARY =========== -->
<ul class="blockList">
<li class="blockList"><a name="method_summary">
<!-- -->
</a>
<h3>Method Summary</h3>
<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation">
<caption><span>Methods</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
</tr>
<tr class="altColor">
<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>
</td>
</tr>
</table>
<ul class="blockList">
<li class="blockList"><a name="methods_inherited_from_class_java.lang.Object">
<!-- -->
</a>
<h3>Methods inherited from class java.lang.<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
<code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long,%20int)" title="class or interface in java.lang">wait</a></code></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
<div class="details">
<ul class="blockList">
<li class="blockList">
<!-- ========= CONSTRUCTOR DETAIL ======== -->
<ul class="blockList">
<li class="blockList"><a name="constructor_detail">
<!-- -->
</a>
<h3>Constructor Detail</h3>
<a name="RootsOfUnity()">
<!-- -->
</a>
<ul class="blockListLast">
<li class="blockList">
<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>
</ul>
<!-- ============ METHOD DETAIL ========== -->
<ul class="blockList">
<li class="blockList"><a name="method_detail">
<!-- -->
</a>
<h3>Method Detail</h3>
<a name="isCounterClockWise()">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<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)">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<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>
</ul>
<a name="getReal(int)">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<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>
<a name="getImaginary(int)">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<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()">
<!-- -->
</a>
<ul class="blockListLast">
<li class="blockList">
<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>
</li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
<!-- ========= END OF CLASS DATA ========= -->
<!-- ======= START OF BOTTOM NAVBAR ====== -->
<div class="bottomNav"><a name="navbar_bottom">
<!-- -->
</a><a href="#skip-navbar_bottom" title="Skip navigation links"></a><a name="navbar_bottom_firstrow">
<!-- -->
</a>
<ul class="navList" title="Navigation">
<li><a href="../../../../../overview-summary.html">Overview</a></li>
<li><a href="package-summary.html">Package</a></li>
<li class="navBarCell1Rev">Class</li>
<li><a href="class-use/RootsOfUnity.html">Use</a></li>
<li><a href="package-tree.html">Tree</a></li>
<li><a href="../../../../../deprecated-list.html">Deprecated</a></li>
<li><a href="../../../../../index-all.html">Index</a></li>
<li><a href="../../../../../help-doc.html">Help</a></li>
</ul>
<div class="aboutLanguage"><em><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script></em></div>
</div>
<div class="subNav">
<ul class="navList">
<li><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex"><span class="strong">Prev Class</span></a></li>
<li>Next Class</li>
</ul>
<ul class="navList">
<li><a href="../../../../../index.html?org/apache/commons/math3/complex/RootsOfUnity.html" target="_top">Frames</a></li>
<li><a href="RootsOfUnity.html" target="_top">No Frames</a></li>
</ul>
<ul class="navList" id="allclasses_navbar_bottom">
<li><a href="../../../../../allclasses-noframe.html">All Classes</a></li>
</ul>
<div>
<script type="text/javascript"><!--
allClassesLink = document.getElementById("allclasses_navbar_bottom");
if(window==top) {
allClassesLink.style.display = "block";
}
else {
allClassesLink.style.display = "none";
}
//-->
</script>
</div>
<div>
<ul class="subNavList">
<li>Summary: </li>
<li>Nested | </li>
<li>Field | </li>
<li><a href="#constructor_summary">Constr</a> | </li>
<li><a href="#method_summary">Method</a></li>
</ul>
<ul class="subNavList">
<li>Detail: </li>
<li>Field | </li>
<li><a href="#constructor_detail">Constr</a> | </li>
<li><a href="#method_detail">Method</a></li>
</ul>
</div>
<a name="skip-navbar_bottom">
<!-- -->
</a></div>
<!-- ======== END OF BOTTOM NAVBAR ======= -->
<p class="legalCopy"><small>Copyright © 2003–2016 <a href="http://www.apache.org/">The Apache Software Foundation</a>. All rights reserved.</small></p>
</body>
</html>
|
