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QRDecomposition (Java Machine Learning Library 0.0.11)
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gov.nist.math.jama</FONT>
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Class QRDecomposition</H2>
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java.lang.Object
<IMG SRC="../../../../resources/inherit.gif" ALT="extended by "><B>gov.nist.math.jama.QRDecomposition</B>
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<DT><PRE>public class <B>QRDecomposition</B><DT>extends java.lang.Object</DL>
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<P>
QR Decomposition.<P> For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n orthogonal matrix Q and an n-by-n upper triangular matrix R so that A = Q*R.<P> The QR decompostion always exists, even if the matrix does not have full rank, so the constructor will never fail. The primary use of the QR decomposition is in the least squares solution of nonsquare systems of simultaneous linear equations. This will fail if isFullRank() returns false.
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<TD><CODE><B><A HREF="../../../../gov/nist/math/jama/QRDecomposition.html#QRDecomposition(gov.nist.math.jama.Matrix)">QRDecomposition</A></B>(<A HREF="../../../../gov/nist/math/jama/Matrix.html" title="class in gov.nist.math.jama">Matrix</A> A)</CODE>
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QR Decomposition, computed by Householder reflections.</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/QRDecomposition.html#getH()">getH</A></B>()</CODE>
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Return the Householder 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/QRDecomposition.html#getQ()">getQ</A></B>()</CODE>
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Generate and return the (economy-sized) orthogonal factor</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/QRDecomposition.html#getR()">getR</A></B>()</CODE>
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Return the upper triangular factor</TD>
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<CODE> boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../gov/nist/math/jama/QRDecomposition.html#isFullRank()">isFullRank</A></B>()</CODE>
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Is the matrix full rank?</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/QRDecomposition.html#solve(gov.nist.math.jama.Matrix)">solve</A></B>(<A HREF="../../../../gov/nist/math/jama/Matrix.html" title="class in gov.nist.math.jama">Matrix</A> B)</CODE>
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Least squares solution of A*X = B</TD>
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<A NAME="QRDecomposition(gov.nist.math.jama.Matrix)"><!-- --></A><H3>
QRDecomposition</H3>
<PRE>
public <B>QRDecomposition</B>(<A HREF="../../../../gov/nist/math/jama/Matrix.html" title="class in gov.nist.math.jama">Matrix</A> A)</PRE>
<DL>
<DD>QR Decomposition, computed by Householder reflections.
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<DT><B>Parameters:</B><DD><CODE>A</CODE> - Rectangular matrix</DL>
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<A NAME="isFullRank()"><!-- --></A><H3>
isFullRank</H3>
<PRE>
public boolean <B>isFullRank</B>()</PRE>
<DL>
<DD>Is the matrix full rank?
<P>
<DD><DL>
<DT><B>Returns:</B><DD>true if R, and hence A, has full rank.</DL>
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<A NAME="getH()"><!-- --></A><H3>
getH</H3>
<PRE>
public <A HREF="../../../../gov/nist/math/jama/Matrix.html" title="class in gov.nist.math.jama">Matrix</A> <B>getH</B>()</PRE>
<DL>
<DD>Return the Householder vectors
<P>
<DD><DL>
<DT><B>Returns:</B><DD>Lower trapezoidal matrix whose columns define the reflections</DL>
</DD>
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<HR>
<A NAME="getR()"><!-- --></A><H3>
getR</H3>
<PRE>
public <A HREF="../../../../gov/nist/math/jama/Matrix.html" title="class in gov.nist.math.jama">Matrix</A> <B>getR</B>()</PRE>
<DL>
<DD>Return the upper triangular factor
<P>
<DD><DL>
<DT><B>Returns:</B><DD>R</DL>
</DD>
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<A NAME="getQ()"><!-- --></A><H3>
getQ</H3>
<PRE>
public <A HREF="../../../../gov/nist/math/jama/Matrix.html" title="class in gov.nist.math.jama">Matrix</A> <B>getQ</B>()</PRE>
<DL>
<DD>Generate and return the (economy-sized) orthogonal factor
<P>
<DD><DL>
<DT><B>Returns:</B><DD>Q</DL>
</DD>
</DL>
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<A NAME="solve(gov.nist.math.jama.Matrix)"><!-- --></A><H3>
solve</H3>
<PRE>
public <A HREF="../../../../gov/nist/math/jama/Matrix.html" title="class in gov.nist.math.jama">Matrix</A> <B>solve</B>(<A HREF="../../../../gov/nist/math/jama/Matrix.html" title="class in gov.nist.math.jama">Matrix</A> B)</PRE>
<DL>
<DD>Least squares solution of A*X = B
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>B</CODE> - A Matrix with as many rows as A and any number of columns.
<DT><B>Returns:</B><DD>X that minimizes the two norm of Q*R*X-B.
<DT><B>Throws:</B>
<DD><CODE>java.lang.IllegalArgumentException</CODE> - Matrix row dimensions must agree.
<DD><CODE>java.lang.RuntimeException</CODE> - Matrix is rank deficient.</DL>
</DD>
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