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
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<!-- NewPage -->
<html lang="en">
<head>
<!-- Generated by javadoc (version 1.7.0_51) on Wed Sep 16 15:55:09 PDT 2015 -->
<title>RowMatrix</title>
<meta name="date" content="2015-09-16">
<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="RowMatrix";
}
//-->
</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="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>
<div class="subNav">
<ul class="navList">
<li><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/MatrixEntry.html" title="class in org.apache.spark.mllib.linalg.distributed"><span class="strong">Prev Class</span></a></li>
<li>Next Class</li>
</ul>
<ul class="navList">
<li><a href="../../../../../../index.html?org/apache/spark/mllib/linalg/distributed/RowMatrix.html" target="_top">Frames</a></li>
<li><a href="RowMatrix.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.spark.mllib.linalg.distributed</div>
<h2 title="Class RowMatrix" class="title">Class RowMatrix</h2>
</div>
<div class="contentContainer">
<ul class="inheritance">
<li>java.lang.Object</li>
<li>
<ul class="inheritance">
<li>org.apache.spark.mllib.linalg.distributed.RowMatrix</li>
</ul>
</li>
</ul>
<div class="description">
<ul class="blockList">
<li class="blockList">
<dl>
<dt>All Implemented Interfaces:</dt>
<dd>java.io.Serializable, <a href="../../../../../../org/apache/spark/Logging.html" title="interface in org.apache.spark">Logging</a>, <a href="../../../../../../org/apache/spark/mllib/linalg/distributed/DistributedMatrix.html" title="interface in org.apache.spark.mllib.linalg.distributed">DistributedMatrix</a></dd>
</dl>
<hr>
<br>
<pre>public class <span class="strong">RowMatrix</span>
extends java.lang.Object
implements <a href="../../../../../../org/apache/spark/mllib/linalg/distributed/DistributedMatrix.html" title="interface in org.apache.spark.mllib.linalg.distributed">DistributedMatrix</a>, <a href="../../../../../../org/apache/spark/Logging.html" title="interface in org.apache.spark">Logging</a></pre>
<div class="block">:: Experimental ::
Represents a row-oriented distributed Matrix with no meaningful row indices.
<p>
param: rows rows stored as an RDD[Vector]
param: nRows number of rows. A non-positive value means unknown, and then the number of rows will
be determined by the number of records in the RDD <code>rows</code>.
param: nCols number of columns. A non-positive value means unknown, and then the number of
columns will be determined by the size of the first row.</div>
<dl><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../serialized-form.html#org.apache.spark.mllib.linalg.distributed.RowMatrix">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/spark/mllib/linalg/distributed/RowMatrix.html#RowMatrix(org.apache.spark.rdd.RDD)">RowMatrix</a></strong>(<a href="../../../../../../org/apache/spark/rdd/RDD.html" title="class in org.apache.spark.rdd">RDD</a><<a href="../../../../../../org/apache/spark/mllib/linalg/Vector.html" title="interface in org.apache.spark.mllib.linalg">Vector</a>> rows)</code>
<div class="block">Alternative constructor leaving matrix dimensions to be determined automatically.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colOne"><code><strong><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html#RowMatrix(org.apache.spark.rdd.RDD, long, int)">RowMatrix</a></strong>(<a href="../../../../../../org/apache/spark/rdd/RDD.html" title="class in org.apache.spark.rdd">RDD</a><<a href="../../../../../../org/apache/spark/mllib/linalg/Vector.html" title="interface in org.apache.spark.mllib.linalg">Vector</a>> rows,
long nRows,
int nCols)</code> </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><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/CoordinateMatrix.html" title="class in org.apache.spark.mllib.linalg.distributed">CoordinateMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html#columnSimilarities()">columnSimilarities</a></strong>()</code>
<div class="block">Compute all cosine similarities between columns of this matrix using the brute-force
approach of computing normalized dot products.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/CoordinateMatrix.html" title="class in org.apache.spark.mllib.linalg.distributed">CoordinateMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html#columnSimilarities(double)">columnSimilarities</a></strong>(double threshold)</code>
<div class="block">Compute similarities between columns of this matrix using a sampling approach.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/spark/mllib/stat/MultivariateStatisticalSummary.html" title="interface in org.apache.spark.mllib.stat">MultivariateStatisticalSummary</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html#computeColumnSummaryStatistics()">computeColumnSummaryStatistics</a></strong>()</code>
<div class="block">Computes column-wise summary statistics.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/spark/mllib/linalg/Matrix.html" title="interface in org.apache.spark.mllib.linalg">Matrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html#computeCovariance()">computeCovariance</a></strong>()</code>
<div class="block">Computes the covariance matrix, treating each row as an observation.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/spark/mllib/linalg/Matrix.html" title="interface in org.apache.spark.mllib.linalg">Matrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html#computeGramianMatrix()">computeGramianMatrix</a></strong>()</code>
<div class="block">Computes the Gramian matrix <code>A^T A</code>.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/spark/mllib/linalg/Matrix.html" title="interface in org.apache.spark.mllib.linalg">Matrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html#computePrincipalComponents(int)">computePrincipalComponents</a></strong>(int k)</code>
<div class="block">Computes the top k principal components.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/spark/mllib/linalg/SingularValueDecomposition.html" title="class in org.apache.spark.mllib.linalg">SingularValueDecomposition</a><<a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html" title="class in org.apache.spark.mllib.linalg.distributed">RowMatrix</a>,<a href="../../../../../../org/apache/spark/mllib/linalg/Matrix.html" title="interface in org.apache.spark.mllib.linalg">Matrix</a>></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html#computeSVD(int, boolean, double)">computeSVD</a></strong>(int k,
boolean computeU,
double rCond)</code>
<div class="block">Computes singular value decomposition of this matrix.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html" title="class in org.apache.spark.mllib.linalg.distributed">RowMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html#multiply(org.apache.spark.mllib.linalg.Matrix)">multiply</a></strong>(<a href="../../../../../../org/apache/spark/mllib/linalg/Matrix.html" title="interface in org.apache.spark.mllib.linalg">Matrix</a> B)</code>
<div class="block">Multiply this matrix by a local matrix on the right.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>long</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html#numCols()">numCols</a></strong>()</code>
<div class="block">Gets or computes the number of columns.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>long</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html#numRows()">numRows</a></strong>()</code>
<div class="block">Gets or computes the number of rows.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/spark/rdd/RDD.html" title="class in org.apache.spark.rdd">RDD</a><<a href="../../../../../../org/apache/spark/mllib/linalg/Vector.html" title="interface in org.apache.spark.mllib.linalg">Vector</a>></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html#rows()">rows</a></strong>()</code> </td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/spark/mllib/linalg/QRDecomposition.html" title="class in org.apache.spark.mllib.linalg">QRDecomposition</a><<a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html" title="class in org.apache.spark.mllib.linalg.distributed">RowMatrix</a>,<a href="../../../../../../org/apache/spark/mllib/linalg/Matrix.html" title="interface in org.apache.spark.mllib.linalg">Matrix</a>></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html#tallSkinnyQR(boolean)">tallSkinnyQR</a></strong>(boolean computeQ)</code>
<div class="block">Compute QR decomposition for <a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html" title="class in org.apache.spark.mllib.linalg.distributed"><code>RowMatrix</code></a>.</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.Object</h3>
<code>clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait</code></li>
</ul>
<ul class="blockList">
<li class="blockList"><a name="methods_inherited_from_class_org.apache.spark.Logging">
<!-- -->
</a>
<h3>Methods inherited from interface org.apache.spark.<a href="../../../../../../org/apache/spark/Logging.html" title="interface in org.apache.spark">Logging</a></h3>
<code><a href="../../../../../../org/apache/spark/Logging.html#initializeIfNecessary()">initializeIfNecessary</a>, <a href="../../../../../../org/apache/spark/Logging.html#initializeLogging()">initializeLogging</a>, <a href="../../../../../../org/apache/spark/Logging.html#isTraceEnabled()">isTraceEnabled</a>, <a href="../../../../../../org/apache/spark/Logging.html#log_()">log_</a>, <a href="../../../../../../org/apache/spark/Logging.html#log()">log</a>, <a href="../../../../../../org/apache/spark/Logging.html#logDebug(scala.Function0)">logDebug</a>, <a href="../../../../../../org/apache/spark/Logging.html#logDebug(scala.Function0, java.lang.Throwable)">logDebug</a>, <a href="../../../../../../org/apache/spark/Logging.html#logError(scala.Function0)">logError</a>, <a href="../../../../../../org/apache/spark/Logging.html#logError(scala.Function0, java.lang.Throwable)">logError</a>, <a href="../../../../../../org/apache/spark/Logging.html#logInfo(scala.Function0)">logInfo</a>, <a href="../../../../../../org/apache/spark/Logging.html#logInfo(scala.Function0, java.lang.Throwable)">logInfo</a>, <a href="../../../../../../org/apache/spark/Logging.html#logName()">logName</a>, <a href="../../../../../../org/apache/spark/Logging.html#logTrace(scala.Function0)">logTrace</a>, <a href="../../../../../../org/apache/spark/Logging.html#logTrace(scala.Function0, java.lang.Throwable)">logTrace</a>, <a href="../../../../../../org/apache/spark/Logging.html#logWarning(scala.Function0)">logWarning</a>, <a href="../../../../../../org/apache/spark/Logging.html#logWarning(scala.Function0, java.lang.Throwable)">logWarning</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="RowMatrix(org.apache.spark.rdd.RDD, long, int)">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>RowMatrix</h4>
<pre>public RowMatrix(<a href="../../../../../../org/apache/spark/rdd/RDD.html" title="class in org.apache.spark.rdd">RDD</a><<a href="../../../../../../org/apache/spark/mllib/linalg/Vector.html" title="interface in org.apache.spark.mllib.linalg">Vector</a>> rows,
long nRows,
int nCols)</pre>
</li>
</ul>
<a name="RowMatrix(org.apache.spark.rdd.RDD)">
<!-- -->
</a>
<ul class="blockListLast">
<li class="blockList">
<h4>RowMatrix</h4>
<pre>public RowMatrix(<a href="../../../../../../org/apache/spark/rdd/RDD.html" title="class in org.apache.spark.rdd">RDD</a><<a href="../../../../../../org/apache/spark/mllib/linalg/Vector.html" title="interface in org.apache.spark.mllib.linalg">Vector</a>> rows)</pre>
<div class="block">Alternative constructor leaving matrix dimensions to be determined automatically.</div>
</li>
</ul>
</li>
</ul>
<!-- ============ METHOD DETAIL ========== -->
<ul class="blockList">
<li class="blockList"><a name="method_detail">
<!-- -->
</a>
<h3>Method Detail</h3>
<a name="rows()">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>rows</h4>
<pre>public <a href="../../../../../../org/apache/spark/rdd/RDD.html" title="class in org.apache.spark.rdd">RDD</a><<a href="../../../../../../org/apache/spark/mllib/linalg/Vector.html" title="interface in org.apache.spark.mllib.linalg">Vector</a>> rows()</pre>
</li>
</ul>
<a name="numCols()">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>numCols</h4>
<pre>public long numCols()</pre>
<div class="block">Gets or computes the number of columns.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/DistributedMatrix.html#numCols()">numCols</a></code> in interface <code><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/DistributedMatrix.html" title="interface in org.apache.spark.mllib.linalg.distributed">DistributedMatrix</a></code></dd>
</dl>
</li>
</ul>
<a name="numRows()">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>numRows</h4>
<pre>public long numRows()</pre>
<div class="block">Gets or computes the number of rows.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/DistributedMatrix.html#numRows()">numRows</a></code> in interface <code><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/DistributedMatrix.html" title="interface in org.apache.spark.mllib.linalg.distributed">DistributedMatrix</a></code></dd>
</dl>
</li>
</ul>
<a name="computeGramianMatrix()">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>computeGramianMatrix</h4>
<pre>public <a href="../../../../../../org/apache/spark/mllib/linalg/Matrix.html" title="interface in org.apache.spark.mllib.linalg">Matrix</a> computeGramianMatrix()</pre>
<div class="block">Computes the Gramian matrix <code>A^T A</code>.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>(undocumented)</dd></dl>
</li>
</ul>
<a name="computeSVD(int, boolean, double)">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>computeSVD</h4>
<pre>public <a href="../../../../../../org/apache/spark/mllib/linalg/SingularValueDecomposition.html" title="class in org.apache.spark.mllib.linalg">SingularValueDecomposition</a><<a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html" title="class in org.apache.spark.mllib.linalg.distributed">RowMatrix</a>,<a href="../../../../../../org/apache/spark/mllib/linalg/Matrix.html" title="interface in org.apache.spark.mllib.linalg">Matrix</a>> computeSVD(int k,
boolean computeU,
double rCond)</pre>
<div class="block">Computes singular value decomposition of this matrix. Denote this matrix by A (m x n). This
will compute matrices U, S, V such that A ~= U * S * V', where S contains the leading k
singular values, U and V contain the corresponding singular vectors.
<p>
At most k largest non-zero singular values and associated vectors are returned. If there are k
such values, then the dimensions of the return will be:
- U is a RowMatrix of size m x k that satisfies U' * U = eye(k),
- s is a Vector of size k, holding the singular values in descending order,
- V is a Matrix of size n x k that satisfies V' * V = eye(k).
<p>
We assume n is smaller than m. The singular values and the right singular vectors are derived
from the eigenvalues and the eigenvectors of the Gramian matrix A' * A. U, the matrix
storing the right singular vectors, is computed via matrix multiplication as
U = A * (V * S^-1^), if requested by user. The actual method to use is determined
automatically based on the cost:
- If n is small (n &lt; 100) or k is large compared with n (k &gt; n / 2), we compute
the Gramian matrix first and then compute its top eigenvalues and eigenvectors locally
on the driver. This requires a single pass with O(n^2^) storage on each executor and
on the driver, and O(n^2^ k) time on the driver.
- Otherwise, we compute (A' * A) * v in a distributive way and send it to ARPACK's DSAUPD to
compute (A' * A)'s top eigenvalues and eigenvectors on the driver node. This requires O(k)
passes, O(n) storage on each executor, and O(n k) storage on the driver.
<p>
Several internal parameters are set to default values. The reciprocal condition number rCond
is set to 1e-9. All singular values smaller than rCond * sigma(0) are treated as zeros, where
sigma(0) is the largest singular value. The maximum number of Arnoldi update iterations for
ARPACK is set to 300 or k * 3, whichever is larger. The numerical tolerance for ARPACK's
eigen-decomposition is set to 1e-10.
<p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>k</code> - number of leading singular values to keep (0 &lt; k &lt;= n).
It might return less than k if
there are numerically zero singular values or there are not enough Ritz values
converged before the maximum number of Arnoldi update iterations is reached (in case
that matrix A is ill-conditioned).</dd><dd><code>computeU</code> - whether to compute U</dd><dd><code>rCond</code> - the reciprocal condition number. All singular values smaller than rCond * sigma(0)
are treated as zero, where sigma(0) is the largest singular value.</dd>
<dt><span class="strong">Returns:</span></dt><dd>SingularValueDecomposition(U, s, V). U = null if computeU = false.</dd></dl>
</li>
</ul>
<a name="computeCovariance()">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>computeCovariance</h4>
<pre>public <a href="../../../../../../org/apache/spark/mllib/linalg/Matrix.html" title="interface in org.apache.spark.mllib.linalg">Matrix</a> computeCovariance()</pre>
<div class="block">Computes the covariance matrix, treating each row as an observation.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>a local dense matrix of size n x n</dd></dl>
</li>
</ul>
<a name="computePrincipalComponents(int)">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>computePrincipalComponents</h4>
<pre>public <a href="../../../../../../org/apache/spark/mllib/linalg/Matrix.html" title="interface in org.apache.spark.mllib.linalg">Matrix</a> computePrincipalComponents(int k)</pre>
<div class="block">Computes the top k principal components.
Rows correspond to observations and columns correspond to variables.
The principal components are stored a local matrix of size n-by-k.
Each column corresponds for one principal component,
and the columns are in descending order of component variance.
The row data do not need to be "centered" first; it is not necessary for
the mean of each column to be 0.
<p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>k</code> - number of top principal components.</dd>
<dt><span class="strong">Returns:</span></dt><dd>a matrix of size n-by-k, whose columns are principal components</dd></dl>
</li>
</ul>
<a name="computeColumnSummaryStatistics()">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>computeColumnSummaryStatistics</h4>
<pre>public <a href="../../../../../../org/apache/spark/mllib/stat/MultivariateStatisticalSummary.html" title="interface in org.apache.spark.mllib.stat">MultivariateStatisticalSummary</a> computeColumnSummaryStatistics()</pre>
<div class="block">Computes column-wise summary statistics.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>(undocumented)</dd></dl>
</li>
</ul>
<a name="multiply(org.apache.spark.mllib.linalg.Matrix)">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>multiply</h4>
<pre>public <a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html" title="class in org.apache.spark.mllib.linalg.distributed">RowMatrix</a> multiply(<a href="../../../../../../org/apache/spark/mllib/linalg/Matrix.html" title="interface in org.apache.spark.mllib.linalg">Matrix</a> B)</pre>
<div class="block">Multiply this matrix by a local matrix on the right.
<p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>B</code> - a local matrix whose number of rows must match the number of columns of this matrix</dd>
<dt><span class="strong">Returns:</span></dt><dd>a <a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html" title="class in org.apache.spark.mllib.linalg.distributed"><code>RowMatrix</code></a> representing the product,
which preserves partitioning</dd></dl>
</li>
</ul>
<a name="columnSimilarities()">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>columnSimilarities</h4>
<pre>public <a href="../../../../../../org/apache/spark/mllib/linalg/distributed/CoordinateMatrix.html" title="class in org.apache.spark.mllib.linalg.distributed">CoordinateMatrix</a> columnSimilarities()</pre>
<div class="block">Compute all cosine similarities between columns of this matrix using the brute-force
approach of computing normalized dot products.
<p></div>
<dl><dt><span class="strong">Returns:</span></dt><dd>An n x n sparse upper-triangular matrix of cosine similarities between
columns of this matrix.</dd></dl>
</li>
</ul>
<a name="columnSimilarities(double)">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>columnSimilarities</h4>
<pre>public <a href="../../../../../../org/apache/spark/mllib/linalg/distributed/CoordinateMatrix.html" title="class in org.apache.spark.mllib.linalg.distributed">CoordinateMatrix</a> columnSimilarities(double threshold)</pre>
<div class="block">Compute similarities between columns of this matrix using a sampling approach.
<p>
The threshold parameter is a trade-off knob between estimate quality and computational cost.
<p>
Setting a threshold of 0 guarantees deterministic correct results, but comes at exactly
the same cost as the brute-force approach. Setting the threshold to positive values
incurs strictly less computational cost than the brute-force approach, however the
similarities computed will be estimates.
<p>
The sampling guarantees relative-error correctness for those pairs of columns that have
similarity greater than the given similarity threshold.
<p>
To describe the guarantee, we set some notation:
Let A be the smallest in magnitude non-zero element of this matrix.
Let B be the largest in magnitude non-zero element of this matrix.
Let L be the maximum number of non-zeros per row.
<p>
For example, for {0,1} matrices: A=B=1.
Another example, for the Netflix matrix: A=1, B=5
<p>
For those column pairs that are above the threshold,
the computed similarity is correct to within 20% relative error with probability
at least 1 - (0.981)^10/B^
<p>
The shuffle size is bounded by the *smaller* of the following two expressions:
<p>
O(n log(n) L / (threshold * A))
O(m L^2^)
<p>
The latter is the cost of the brute-force approach, so for non-zero thresholds,
the cost is always cheaper than the brute-force approach.
<p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>threshold</code> - Set to 0 for deterministic guaranteed correctness.
Similarities above this threshold are estimated
with the cost vs estimate quality trade-off described above.</dd>
<dt><span class="strong">Returns:</span></dt><dd>An n x n sparse upper-triangular matrix of cosine similarities
between columns of this matrix.</dd></dl>
</li>
</ul>
<a name="tallSkinnyQR(boolean)">
<!-- -->
</a>
<ul class="blockListLast">
<li class="blockList">
<h4>tallSkinnyQR</h4>
<pre>public <a href="../../../../../../org/apache/spark/mllib/linalg/QRDecomposition.html" title="class in org.apache.spark.mllib.linalg">QRDecomposition</a><<a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html" title="class in org.apache.spark.mllib.linalg.distributed">RowMatrix</a>,<a href="../../../../../../org/apache/spark/mllib/linalg/Matrix.html" title="interface in org.apache.spark.mllib.linalg">Matrix</a>> tallSkinnyQR(boolean computeQ)</pre>
<div class="block">Compute QR decomposition for <a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html" title="class in org.apache.spark.mllib.linalg.distributed"><code>RowMatrix</code></a>. The implementation is designed to optimize the QR
decomposition (factorization) for the <a href="../../../../../../org/apache/spark/mllib/linalg/distributed/RowMatrix.html" title="class in org.apache.spark.mllib.linalg.distributed"><code>RowMatrix</code></a> of a tall and skinny shape.
Reference:
Paul G. Constantine, David F. Gleich. "Tall and skinny QR factorizations in MapReduce
architectures" (<code>http://dx.doi.org/10.1145/1996092.1996103</code>)
<p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>computeQ</code> - whether to computeQ</dd>
<dt><span class="strong">Returns:</span></dt><dd>QRDecomposition(Q, R), Q = null if computeQ = false.</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="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>
<div class="subNav">
<ul class="navList">
<li><a href="../../../../../../org/apache/spark/mllib/linalg/distributed/MatrixEntry.html" title="class in org.apache.spark.mllib.linalg.distributed"><span class="strong">Prev Class</span></a></li>
<li>Next Class</li>
</ul>
<ul class="navList">
<li><a href="../../../../../../index.html?org/apache/spark/mllib/linalg/distributed/RowMatrix.html" target="_top">Frames</a></li>
<li><a href="RowMatrix.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 ======= -->
<script defer="defer" type="text/javascript" src="../../../../../../lib/jquery.js"></script><script defer="defer" type="text/javascript" src="../../../../../../lib/api-javadocs.js"></script></body>
</html>
|
