package?Jama;

???/**?Cholesky?Decomposition.
???

???For?a?symmetric?positive?definite?matrix?A?the?Cholesky?decomposition
???is?an?lower?triangular?matrix?L?so?that?A?=?L*L‘.
???

???If?the?matrix?is?not?symmetric?or?positive?definite?the?constructor
???returns?a?partial?decomposition?and?sets?an?internal?flag?that?may
???be?queried?by?the?isSPD（）?method.
???*/

public?class?CholeskyDecomposition?implements?java.io.Serializable?{

/*?------------------------
???Class?variables
?*?------------------------?*/

???/**?Array?for?internal?storage?of?decomposition.
???@serial?internal?array?storage.
???*/
???private?double[][]?L;

???/**?Row?and?column?dimension?（square?matrix）.
???@serial?matrix?dimension.
???*/
???private?int?n;

???/**?Symmetric?and?positive?definite?flag.
???@serial?is?symmetric?and?positive?definite?flag.
???*/
???private?boolean?isspd;

/*?------------------------
???Constructor
?*?------------------------?*/

???/**?Cholesky?algorithm?for?symmetric?and?positive?definite?matrix.
???@param??A???Square?symmetric?matrix.
???@return?????Structure?to?access?L?and?isspd?flag.
???*/

???public?CholeskyDecomposition?（Matrix?Arg）?{


?????//?Initialize.
??????double[][]?A?=?Arg.getArray（）;
??????n?=?Arg.getRowDimension（）;
??????L?=?new?double[n][n];
??????isspd?=?（Arg.getColumnDimension（）?==?n）;
??????//?Main?loop.
??????for?（int?j?=?0;?j??????????double[]?Lrowj?=?L[j];
?????????double?d?=?0.0;
?????????for?（int?k?=?0;?k?????????????double[]?Lrowk?=?L[k];
????????????double?s?=?0.0;
????????????for?（int?i?=?0;?i????????????????s?+=?Lrowk[i]*Lrowj[i];
????????????}
????????????Lrowj[k]?=?s?=?（A[j][k]?-?s）/L[k][k];
????????????d?=?d?+?s*s;
????????????isspd?=?isspd?&?（A[k][j]?==?A[j][k]）;?
?????????}
?????????d?=?A[j][j]?-?d;
?????????isspd?=?isspd?&?（d?>?0.0）;
?????????L[j][j]?=?Math.sqrt（Math.max（d0.0））;
?????????for?（int?k?=?j+1;?k?????????????L[j][k]?=?0.0;
?????????}
??????}
???}

/*?------------------------
???Temporary?experimental?code.
?*?------------------------?*\

???\**?Right?Triangular?Cholesky?Decomposition.
???

???For?a?symmetric?positive?definite?matrix?A?the?Right?Cholesky
???decomposition?is?an?upper?triangular?matrix?R?so?that?A?=?R‘*R.
???This?constructor?computes?R?with?the?Fortran?inspired?column?oriented
???algorithm?used?in?LINPACK?and?MATLAB.??In?Java?we?suspect?a?row?oriented
???lower?triangular?decomposition?is?faster.??We?have?temporarily?included
???this?constructor?here?until?timing?experiments?confirm?this?suspicion.
???*\

???\**?Array?for?internal?storage?of?right?triangular?decomposition.?**\
???private?transient?double[][]?R;

???\**?Cholesky?algorithm?for?symmetric?and?positive?definite?matrix.
???@param??A???????????Square?symmetric?matrix.
???@param??rightflag???Actual?value?ignored.
???@return?????????????Structure?to?access?R?and?isspd?flag.

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件????????378??2011-07-22?13:08??AHP\.classpath

?????文件????????791??2011-07-22?10:22??AHP\.myeclipse\profiler\jaccobi.xml

?????文件????????379??2011-07-21?10:48??AHP\.project

?????文件????????629??2011-07-21?10:48??AHP\.settings\org.eclipse.jdt.core.prefs

?????文件???????3126??2011-12-02?15:06??AHP\bin\ahp.class

?????文件???????2965??2011-12-01?11:21??AHP\bin\jaccobi.class

?????文件???????1288??2005-07-13?17:36??AHP\Jama-1.0.2\Jama\ChangeLog

?????文件???????1738??2005-07-13?17:36??AHP\Jama-1.0.2\Jama\CholeskyDecomposition.class

?????文件???????5757??2005-03-04?14:24??AHP\Jama-1.0.2\Jama\CholeskyDecomposition.java

?????文件???????1249??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\allclasses-frame.html

?????文件???????1129??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\allclasses-noframe.html

?????文件???????4784??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\constant-values.html

?????文件???????4720??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\deprecated-list.html

?????文件???????8607??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\help-doc.html

?????文件??????27826??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\index-all.html

?????文件???????1231??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\index.html

?????文件??????11856??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\Jama\CholeskyDecomposition.html

?????文件??????12740??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\Jama\EigenvalueDecomposition.html

?????文件??????14559??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\Jama\LUDecomposition.html

?????文件??????62698??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\Jama\Matrix.html

?????文件???????1368??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\Jama\package-frame.html

?????文件???????6268??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\Jama\package-summary.html

?????文件???????5742??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\Jama\package-tree.html

?????文件??????13483??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\Jama\QRDecomposition.html

?????文件??????14147??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\Jama\SingularValueDecomposition.html

?????文件???????5756??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\overview-tree.html

?????文件??????????6??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\package-list

?????文件?????????57??2005-07-13?17:39??AHP\Jama-1.0.2\Jama\doc\resources\inherit.gif

?????文件??????13333??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\serialized-form.html

?????文件???????1231??2005-07-13?17:40??AHP\Jama-1.0.2\Jama\doc\stylesheet.css

............此處省略45個文件信息