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<H1>IPQRDecomposition</H1>
Compute the QR factorization of a set of vectors.
<H3><FONT COLOR="#883300">Synopsis</FONT></H3>
<PRE>
#include "slepcip.h"
PetscErrorCode IPQRDecomposition(IP ip,Vec *V,PetscInt m,PetscInt n,PetscScalar *R,PetscInt ldr)
</PRE>
Collective on <A HREF="../IP/IP.html#IP">IP</A> and Vec
<P>
<H3><FONT COLOR="#883300">Input Parameters</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>ip </B></TD><TD> - the eigenproblem solver context
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>V </B></TD><TD> - set of vectors
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>m </B></TD><TD> - starting column
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>n </B></TD><TD> - ending column
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>ldr </B></TD><TD> - leading dimension of R
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">Output Parameter</FONT></H3>
<DT><B>R </B> - triangular matrix of QR factorization
<br>
<P>
<H3><FONT COLOR="#883300">Notes</FONT></H3>
This routine orthonormalizes the columns of V so that V'*V=I up to
working precision. It assumes that the first m columns (from 0 to m-1)
are already orthonormal. The coefficients of the orthogonalization are
stored in R so that V*R is equal to the original V.
<P>
In some cases, this routine makes V B-orthonormal, that is, V'*B*V=I.
<P>
If one of the vectors is linearly dependent wrt the rest (at working
precision) then it is replaced by a random vector.
<P>
<P>
<H3><FONT COLOR="#883300">See Also</FONT></H3>
<A HREF="../IP/IPOrthogonalize.html#IPOrthogonalize">IPOrthogonalize</A>(), <A HREF="../IP/IPNorm.html#IPNorm">IPNorm</A>(), <A HREF="../IP/IPInnerProduct.html#IPInnerProduct">IPInnerProduct</A>().
<BR><P><B><FONT COLOR="#883300">Location: </FONT></B><A HREF="../../../src/ip/iporthog.c.html#IPQRDecomposition">src/ip/iporthog.c</A>
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