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90 <H2>
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92 org.apache.commons.math.linear</FONT>
93 <BR>
94 Class CholeskyDecompositionImpl</H2>
95 <PRE>
96 <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
97 <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math.linear.CholeskyDecompositionImpl</B>
98 </PRE>
99 <DL>
100 <DT><B>All Implemented Interfaces:</B> <DD><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecomposition.html" title="interface in org.apache.commons.math.linear">CholeskyDecomposition</A></DD>
101 </DL>
102 <HR>
103 <DL>
104 <DT><PRE>public class <A HREF="../../../../../src-html/org/apache/commons/math/linear/CholeskyDecompositionImpl.html#line.34"><B>CholeskyDecompositionImpl</B></A><DT>extends <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A><DT>implements <A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecomposition.html" title="interface in org.apache.commons.math.linear">CholeskyDecomposition</A></DL>
105 </PRE>
106
107 <P>
108 Calculates the Cholesky decomposition of a matrix.
109 <p>The Cholesky decomposition of a real symmetric positive-definite
110 matrix A consists of a lower triangular matrix L with same size that
111 satisfy: A = LL<sup>T</sup>Q = I). In a sense, this is the square root of A.</p>
112 <P>
113
114 <P>
115 <DL>
116 <DT><B>Since:</B></DT>
117 <DD>2.0</DD>
118 <DT><B>Version:</B></DT>
119 <DD>$Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $</DD>
120 <DT><B>See Also:</B><DD><a href="http://mathworld.wolfram.com/CholeskyDecomposition.html">MathWorld</a>,
121 <a href="http://en.wikipedia.org/wiki/Cholesky_decomposition">Wikipedia</a></DL>
122 <HR>
123
124 <P>
125 <!-- =========== FIELD SUMMARY =========== -->
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133 <TR BGCOLOR="white" CLASS="TableRowColor">
134 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
135 <CODE>static&nbsp;double</CODE></FONT></TD>
136 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD">DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</A></B></CODE>
137
138 <BR>
139 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Default threshold below which diagonal elements are considered null
140 and matrix not positive definite.</TD>
141 </TR>
142 <TR BGCOLOR="white" CLASS="TableRowColor">
143 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
144 <CODE>static&nbsp;double</CODE></FONT></TD>
145 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#DEFAULT_RELATIVE_SYMMETRY_THRESHOLD">DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</A></B></CODE>
146
147 <BR>
148 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Default threshold above which off-diagonal elements are considered too different
149 and matrix not symmetric.</TD>
150 </TR>
151 </TABLE>
152 &nbsp;
153 <!-- ======== CONSTRUCTOR SUMMARY ======== -->
154
155 <A NAME="constructor_summary"><!-- --></A>
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158 <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
159 <B>Constructor Summary</B></FONT></TH>
160 </TR>
161 <TR BGCOLOR="white" CLASS="TableRowColor">
162 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#CholeskyDecompositionImpl(org.apache.commons.math.linear.RealMatrix)">CholeskyDecompositionImpl</A></B>(<A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A>&nbsp;matrix)</CODE>
163
164 <BR>
165 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculates the Cholesky decomposition of the given matrix.</TD>
166 </TR>
167 <TR BGCOLOR="white" CLASS="TableRowColor">
168 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#CholeskyDecompositionImpl(org.apache.commons.math.linear.RealMatrix, double, double)">CholeskyDecompositionImpl</A></B>(<A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A>&nbsp;matrix,
169 double&nbsp;relativeSymmetryThreshold,
170 double&nbsp;absolutePositivityThreshold)</CODE>
171
172 <BR>
173 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculates the Cholesky decomposition of the given matrix.</TD>
174 </TR>
175 </TABLE>
176 &nbsp;
177 <!-- ========== METHOD SUMMARY =========== -->
178
179 <A NAME="method_summary"><!-- --></A>
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183 <B>Method Summary</B></FONT></TH>
184 </TR>
185 <TR BGCOLOR="white" CLASS="TableRowColor">
186 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
187 <CODE>&nbsp;double</CODE></FONT></TD>
188 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#getDeterminant()">getDeterminant</A></B>()</CODE>
189
190 <BR>
191 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Return the determinant of the matrix</TD>
192 </TR>
193 <TR BGCOLOR="white" CLASS="TableRowColor">
194 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
195 <CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A></CODE></FONT></TD>
196 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#getL()">getL</A></B>()</CODE>
197
198 <BR>
199 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the matrix L of the decomposition.</TD>
200 </TR>
201 <TR BGCOLOR="white" CLASS="TableRowColor">
202 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
203 <CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A></CODE></FONT></TD>
204 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#getLT()">getLT</A></B>()</CODE>
205
206 <BR>
207 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the transpose of the matrix L of the decomposition.</TD>
208 </TR>
209 <TR BGCOLOR="white" CLASS="TableRowColor">
210 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
211 <CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math/linear/DecompositionSolver.html" title="interface in org.apache.commons.math.linear">DecompositionSolver</A></CODE></FONT></TD>
212 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#getSolver()">getSolver</A></B>()</CODE>
213
214 <BR>
215 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get a solver for finding the A &times; X = B solution in least square sense.</TD>
216 </TR>
217 </TABLE>
218 &nbsp;<A NAME="methods_inherited_from_class_java.lang.Object"><!-- --></A>
219 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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225 </TR>
226 </TABLE>
227 &nbsp;
228 <P>
229
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236 <B>Field Detail</B></FONT></TH>
237 </TR>
238 </TABLE>
239
240 <A NAME="DEFAULT_RELATIVE_SYMMETRY_THRESHOLD"><!-- --></A><H3>
241 DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</H3>
242 <PRE>
243 public static final double <A HREF="../../../../../src-html/org/apache/commons/math/linear/CholeskyDecompositionImpl.html#line.38"><B>DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</B></A></PRE>
244 <DL>
245 <DD>Default threshold above which off-diagonal elements are considered too different
246 and matrix not symmetric.
247 <P>
248 <DL>
249 <DT><B>See Also:</B><DD><A HREF="../../../../../constant-values.html#org.apache.commons.math.linear.CholeskyDecompositionImpl.DEFAULT_RELATIVE_SYMMETRY_THRESHOLD">Constant Field Values</A></DL>
250 </DL>
251 <HR>
252
253 <A NAME="DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD"><!-- --></A><H3>
254 DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</H3>
255 <PRE>
256 public static final double <A HREF="../../../../../src-html/org/apache/commons/math/linear/CholeskyDecompositionImpl.html#line.42"><B>DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</B></A></PRE>
257 <DL>
258 <DD>Default threshold below which diagonal elements are considered null
259 and matrix not positive definite.
260 <P>
261 <DL>
262 <DT><B>See Also:</B><DD><A HREF="../../../../../constant-values.html#org.apache.commons.math.linear.CholeskyDecompositionImpl.DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD">Constant Field Values</A></DL>
263 </DL>
264
265 <!-- ========= CONSTRUCTOR DETAIL ======== -->
266
267 <A NAME="constructor_detail"><!-- --></A>
268 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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271 <B>Constructor Detail</B></FONT></TH>
272 </TR>
273 </TABLE>
274
275 <A NAME="CholeskyDecompositionImpl(org.apache.commons.math.linear.RealMatrix)"><!-- --></A><H3>
276 CholeskyDecompositionImpl</H3>
277 <PRE>
278 public <A HREF="../../../../../src-html/org/apache/commons/math/linear/CholeskyDecompositionImpl.html#line.71"><B>CholeskyDecompositionImpl</B></A>(<A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A>&nbsp;matrix)
279 throws <A HREF="../../../../../org/apache/commons/math/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math.linear">NonSquareMatrixException</A>,
280 <A HREF="../../../../../org/apache/commons/math/linear/NotSymmetricMatrixException.html" title="class in org.apache.commons.math.linear">NotSymmetricMatrixException</A>,
281 <A HREF="../../../../../org/apache/commons/math/linear/NotPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math.linear">NotPositiveDefiniteMatrixException</A></PRE>
282 <DL>
283 <DD>Calculates the Cholesky decomposition of the given matrix.
284 <p>
285 Calling this constructor is equivalent to call <A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#CholeskyDecompositionImpl(org.apache.commons.math.linear.RealMatrix, double, double)"><CODE>CholeskyDecompositionImpl(RealMatrix, double, double)</CODE></A> with the
286 thresholds set to the default values <A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#DEFAULT_RELATIVE_SYMMETRY_THRESHOLD"><CODE>DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</CODE></A> and <A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD"><CODE>DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</CODE></A>
287 </p>
288 <P>
289 <DL>
290 <DT><B>Parameters:</B><DD><CODE>matrix</CODE> - the matrix to decompose
291 <DT><B>Throws:</B>
292 <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math.linear">NonSquareMatrixException</A></CODE> - if matrix is not square
293 <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/NotSymmetricMatrixException.html" title="class in org.apache.commons.math.linear">NotSymmetricMatrixException</A></CODE> - if matrix is not symmetric
294 <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/NotPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math.linear">NotPositiveDefiniteMatrixException</A></CODE> - if the matrix is not
295 strictly positive definite<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#CholeskyDecompositionImpl(org.apache.commons.math.linear.RealMatrix, double, double)"><CODE>CholeskyDecompositionImpl(RealMatrix, double, double)</CODE></A>,
296 <A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#DEFAULT_RELATIVE_SYMMETRY_THRESHOLD"><CODE>DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</CODE></A>,
297 <A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD"><CODE>DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</CODE></A></DL>
298 </DL>
299 <HR>
300
301 <A NAME="CholeskyDecompositionImpl(org.apache.commons.math.linear.RealMatrix, double, double)"><!-- --></A><H3>
302 CholeskyDecompositionImpl</H3>
303 <PRE>
304 public <A HREF="../../../../../src-html/org/apache/commons/math/linear/CholeskyDecompositionImpl.html#line.93"><B>CholeskyDecompositionImpl</B></A>(<A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A>&nbsp;matrix,
305 double&nbsp;relativeSymmetryThreshold,
306 double&nbsp;absolutePositivityThreshold)
307 throws <A HREF="../../../../../org/apache/commons/math/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math.linear">NonSquareMatrixException</A>,
308 <A HREF="../../../../../org/apache/commons/math/linear/NotSymmetricMatrixException.html" title="class in org.apache.commons.math.linear">NotSymmetricMatrixException</A>,
309 <A HREF="../../../../../org/apache/commons/math/linear/NotPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math.linear">NotPositiveDefiniteMatrixException</A></PRE>
310 <DL>
311 <DD>Calculates the Cholesky decomposition of the given matrix.
312 <P>
313 <DL>
314 <DT><B>Parameters:</B><DD><CODE>matrix</CODE> - the matrix to decompose<DD><CODE>relativeSymmetryThreshold</CODE> - threshold above which off-diagonal
315 elements are considered too different and matrix not symmetric<DD><CODE>absolutePositivityThreshold</CODE> - threshold below which diagonal
316 elements are considered null and matrix not positive definite
317 <DT><B>Throws:</B>
318 <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math.linear">NonSquareMatrixException</A></CODE> - if matrix is not square
319 <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/NotSymmetricMatrixException.html" title="class in org.apache.commons.math.linear">NotSymmetricMatrixException</A></CODE> - if matrix is not symmetric
320 <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/NotPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math.linear">NotPositiveDefiniteMatrixException</A></CODE> - if the matrix is not
321 strictly positive definite<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#CholeskyDecompositionImpl(org.apache.commons.math.linear.RealMatrix)"><CODE>CholeskyDecompositionImpl(RealMatrix)</CODE></A>,
322 <A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#DEFAULT_RELATIVE_SYMMETRY_THRESHOLD"><CODE>DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</CODE></A>,
323 <A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecompositionImpl.html#DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD"><CODE>DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</CODE></A></DL>
324 </DL>
325
326 <!-- ============ METHOD DETAIL ========== -->
327
328 <A NAME="method_detail"><!-- --></A>
329 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
330 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
331 <TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
332 <B>Method Detail</B></FONT></TH>
333 </TR>
334 </TABLE>
335
336 <A NAME="getL()"><!-- --></A><H3>
337 getL</H3>
338 <PRE>
339 public <A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A> <A HREF="../../../../../src-html/org/apache/commons/math/linear/CholeskyDecompositionImpl.html#line.154"><B>getL</B></A>()</PRE>
340 <DL>
341 <DD>Returns the matrix L of the decomposition.
342 <p>L is an lower-triangular matrix</p>
343 <P>
344 <DD><DL>
345 <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecomposition.html#getL()">getL</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecomposition.html" title="interface in org.apache.commons.math.linear">CholeskyDecomposition</A></CODE></DL>
346 </DD>
347 <DD><DL>
348
349 <DT><B>Returns:</B><DD>the L matrix</DL>
350 </DD>
351 </DL>
352 <HR>
353
354 <A NAME="getLT()"><!-- --></A><H3>
355 getLT</H3>
356 <PRE>
357 public <A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A> <A HREF="../../../../../src-html/org/apache/commons/math/linear/CholeskyDecompositionImpl.html#line.162"><B>getLT</B></A>()</PRE>
358 <DL>
359 <DD>Returns the transpose of the matrix L of the decomposition.
360 <p>L<sup>T</sup> is an upper-triangular matrix</p>
361 <P>
362 <DD><DL>
363 <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecomposition.html#getLT()">getLT</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecomposition.html" title="interface in org.apache.commons.math.linear">CholeskyDecomposition</A></CODE></DL>
364 </DD>
365 <DD><DL>
366
367 <DT><B>Returns:</B><DD>the transpose of the matrix L of the decomposition</DL>
368 </DD>
369 </DL>
370 <HR>
371
372 <A NAME="getDeterminant()"><!-- --></A><H3>
373 getDeterminant</H3>
374 <PRE>
375 public double <A HREF="../../../../../src-html/org/apache/commons/math/linear/CholeskyDecompositionImpl.html#line.174"><B>getDeterminant</B></A>()</PRE>
376 <DL>
377 <DD>Return the determinant of the matrix
378 <P>
379 <DD><DL>
380 <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecomposition.html#getDeterminant()">getDeterminant</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecomposition.html" title="interface in org.apache.commons.math.linear">CholeskyDecomposition</A></CODE></DL>
381 </DD>
382 <DD><DL>
383
384 <DT><B>Returns:</B><DD>determinant of the matrix</DL>
385 </DD>
386 </DL>
387 <HR>
388
389 <A NAME="getSolver()"><!-- --></A><H3>
390 getSolver</H3>
391 <PRE>
392 public <A HREF="../../../../../org/apache/commons/math/linear/DecompositionSolver.html" title="interface in org.apache.commons.math.linear">DecompositionSolver</A> <A HREF="../../../../../src-html/org/apache/commons/math/linear/CholeskyDecompositionImpl.html#line.184"><B>getSolver</B></A>()</PRE>
393 <DL>
394 <DD>Get a solver for finding the A &times; X = B solution in least square sense.
395 <P>
396 <DD><DL>
397 <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecomposition.html#getSolver()">getSolver</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/linear/CholeskyDecomposition.html" title="interface in org.apache.commons.math.linear">CholeskyDecomposition</A></CODE></DL>
398 </DD>
399 <DD><DL>
400
401 <DT><B>Returns:</B><DD>a solver</DL>
402 </DD>
403 </DL>
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