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SingularValueDecomposition (Java Machine Learning Library 0.0.11)
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Class SingularValueDecomposition</H2>
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java.lang.Object
<IMG SRC="../../../../resources/inherit.gif" ALT="extended by "><B>gov.nist.math.jama.SingularValueDecomposition</B>
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<DT><PRE>public class <B>SingularValueDecomposition</B><DT>extends java.lang.Object</DL>
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<P>
Singular Value Decomposition. <P> For an m-by-n matrix A with m >= n, the singular value decomposition is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and an n-by-n orthogonal matrix V so that A = U*S*V'. <P> The singular values, sigma[k] = S[k][k], are ordered so that sigma[0] >= sigma[1] >= ... >= sigma[n-1]. <P> The singular value decompostion always exists, so the constructor will never fail. The matrix condition number and the effective numerical rank can be computed from this decomposition.
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<TD><CODE><B><A HREF="../../../../gov/nist/math/jama/SingularValueDecomposition.html#SingularValueDecomposition(gov.nist.math.jama.Matrix)">SingularValueDecomposition</A></B>(<A HREF="../../../../gov/nist/math/jama/Matrix.html" title="class in gov.nist.math.jama">Matrix</A> Arg)</CODE>
<BR>
Construct the singular value decomposition</TD>
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<CODE> double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../gov/nist/math/jama/SingularValueDecomposition.html#cond()">cond</A></B>()</CODE>
<BR>
Two norm condition number</TD>
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<CODE> <A HREF="../../../../gov/nist/math/jama/Matrix.html" title="class in gov.nist.math.jama">Matrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../gov/nist/math/jama/SingularValueDecomposition.html#getS()">getS</A></B>()</CODE>
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Return the diagonal matrix of singular values</TD>
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<CODE> double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../gov/nist/math/jama/SingularValueDecomposition.html#getSingularValues()">getSingularValues</A></B>()</CODE>
<BR>
Return the one-dimensional array of singular values</TD>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE> <A HREF="../../../../gov/nist/math/jama/Matrix.html" title="class in gov.nist.math.jama">Matrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../gov/nist/math/jama/SingularValueDecomposition.html#getU()">getU</A></B>()</CODE>
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Return the left singular vectors</TD>
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<CODE> <A HREF="../../../../gov/nist/math/jama/Matrix.html" title="class in gov.nist.math.jama">Matrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../gov/nist/math/jama/SingularValueDecomposition.html#getV()">getV</A></B>()</CODE>
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Return the right singular vectors</TD>
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<CODE> double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../gov/nist/math/jama/SingularValueDecomposition.html#norm2()">norm2</A></B>()</CODE>
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Two norm</TD>
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<CODE> int</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../gov/nist/math/jama/SingularValueDecomposition.html#rank()">rank</A></B>()</CODE>
<BR>
Effective numerical matrix rank</TD>
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<TD><CODE>clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait</CODE></TD>
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<A NAME="SingularValueDecomposition(gov.nist.math.jama.Matrix)"><!-- --></A><H3>
SingularValueDecomposition</H3>
<PRE>
public <B>SingularValueDecomposition</B>(<A HREF="../../../../gov/nist/math/jama/Matrix.html" title="class in gov.nist.math.jama">Matrix</A> Arg)</PRE>
<DL>
<DD>Construct the singular value decomposition
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<DT><B>Parameters:</B><DD><CODE>A</CODE> - Rectangular matrix</DL>
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<A NAME="getU()"><!-- --></A><H3>
getU</H3>
<PRE>
public <A HREF="../../../../gov/nist/math/jama/Matrix.html" title="class in gov.nist.math.jama">Matrix</A> <B>getU</B>()</PRE>
<DL>
<DD>Return the left singular vectors
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<DD><DL>
<DT><B>Returns:</B><DD>U</DL>
</DD>
</DL>
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<A NAME="getV()"><!-- --></A><H3>
getV</H3>
<PRE>
public <A HREF="../../../../gov/nist/math/jama/Matrix.html" title="class in gov.nist.math.jama">Matrix</A> <B>getV</B>()</PRE>
<DL>
<DD>Return the right singular vectors
<P>
<DD><DL>
<DT><B>Returns:</B><DD>V</DL>
</DD>
</DL>
<HR>
<A NAME="getSingularValues()"><!-- --></A><H3>
getSingularValues</H3>
<PRE>
public double[] <B>getSingularValues</B>()</PRE>
<DL>
<DD>Return the one-dimensional array of singular values
<P>
<DD><DL>
<DT><B>Returns:</B><DD>diagonal of S.</DL>
</DD>
</DL>
<HR>
<A NAME="getS()"><!-- --></A><H3>
getS</H3>
<PRE>
public <A HREF="../../../../gov/nist/math/jama/Matrix.html" title="class in gov.nist.math.jama">Matrix</A> <B>getS</B>()</PRE>
<DL>
<DD>Return the diagonal matrix of singular values
<P>
<DD><DL>
<DT><B>Returns:</B><DD>S</DL>
</DD>
</DL>
<HR>
<A NAME="norm2()"><!-- --></A><H3>
norm2</H3>
<PRE>
public double <B>norm2</B>()</PRE>
<DL>
<DD>Two norm
<P>
<DD><DL>
<DT><B>Returns:</B><DD>max(S)</DL>
</DD>
</DL>
<HR>
<A NAME="cond()"><!-- --></A><H3>
cond</H3>
<PRE>
public double <B>cond</B>()</PRE>
<DL>
<DD>Two norm condition number
<P>
<DD><DL>
<DT><B>Returns:</B><DD>max(S)/min(S)</DL>
</DD>
</DL>
<HR>
<A NAME="rank()"><!-- --></A><H3>
rank</H3>
<PRE>
public int <B>rank</B>()</PRE>
<DL>
<DD>Effective numerical matrix rank
<P>
<DD><DL>
<DT><B>Returns:</B><DD>Number of nonnegligible singular values.</DL>
</DD>
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