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QRDecomposition
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Jama</FONT>
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Class QRDecomposition</H2>
<PRE>
java.lang.Object
<IMG SRC="../resources/inherit.gif" ALT="extended by "><B>Jama.QRDecomposition</B>
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<DL>
<DT><B>All Implemented Interfaces:</B> <DD>java.io.Serializable</DD>
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<DT><PRE>public class <B>QRDecomposition</B><DT>extends java.lang.Object<DT>implements java.io.Serializable</DL>
</PRE>
<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.
<P>
<P>
<DL>
<DT><B>See Also:</B><DD><A HREF="../serialized-form.html#Jama.QRDecomposition">Serialized Form</A></DL>
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<TD><CODE><B><A HREF="../Jama/QRDecomposition.html#QRDecomposition(Jama.Matrix)">QRDecomposition</A></B>(<A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A> A)</CODE>
<BR>
QR Decomposition, computed by Householder reflections.</TD>
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<CODE> <A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../Jama/QRDecomposition.html#getH()">getH</A></B>()</CODE>
<BR>
Return the Householder vectors</TD>
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<CODE> <A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../Jama/QRDecomposition.html#getQ()">getQ</A></B>()</CODE>
<BR>
Generate and return the (economy-sized) orthogonal factor</TD>
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<CODE> <A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../Jama/QRDecomposition.html#getR()">getR</A></B>()</CODE>
<BR>
Return the upper triangular factor</TD>
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<CODE> boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../Jama/QRDecomposition.html#isFullRank()">isFullRank</A></B>()</CODE>
<BR>
Is the matrix full rank?</TD>
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<CODE> <A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../Jama/QRDecomposition.html#solve(Jama.Matrix)">solve</A></B>(<A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A> B)</CODE>
<BR>
Least squares solution of A*X = B</TD>
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<A NAME="QRDecomposition(Jama.Matrix)"><!-- --></A><H3>
QRDecomposition</H3>
<PRE>
public <B>QRDecomposition</B>(<A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A> A)</PRE>
<DL>
<DD>QR Decomposition, computed by Householder reflections.
<P>
<DL>
<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>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>true if R, and hence A, has full rank.</DL>
</DD>
</DL>
<HR>
<A NAME="getH()"><!-- --></A><H3>
getH</H3>
<PRE>
public <A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A> <B>getH</B>()</PRE>
<DL>
<DD>Return the Householder vectors
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>Lower trapezoidal matrix whose columns define the reflections</DL>
</DD>
</DL>
<HR>
<A NAME="getR()"><!-- --></A><H3>
getR</H3>
<PRE>
public <A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A> <B>getR</B>()</PRE>
<DL>
<DD>Return the upper triangular factor
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>R</DL>
</DD>
</DL>
<HR>
<A NAME="getQ()"><!-- --></A><H3>
getQ</H3>
<PRE>
public <A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A> <B>getQ</B>()</PRE>
<DL>
<DD>Generate and return the (economy-sized) orthogonal factor
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>Q</DL>
</DD>
</DL>
<HR>
<A NAME="solve(Jama.Matrix)"><!-- --></A><H3>
solve</H3>
<PRE>
public <A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A> <B>solve</B>(<A HREF="../Jama/Matrix.html" title="class in Jama">Matrix</A> B)</PRE>
<DL>
<DD>Least squares solution of A*X = B
<P>
<DD><DL>
</DL>
</DD>
<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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