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<div id="version" align=right><b>slepc-3.7.3 2016-09-29</b></div>
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<H1>BVOrthogonalize</H1>
Orthogonalize all columns (except leading ones), that is, compute the QR decomposition.
<H3><FONT COLOR="#883300">Synopsis</FONT></H3>
<PRE>
#include "slepcbv.h"
PetscErrorCode BVOrthogonalize(BV V,Mat R)
</PRE>
Collective on <A HREF="../BV/BV.html#BV">BV</A>
<P>
<H3><FONT COLOR="#883300">Input Parameter</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0"><TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>V </B></TD><TD> - basis vectors
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">Output Parameters</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>V </B></TD><TD> - the modified basis vectors
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>R </B></TD><TD> - a sequential dense matrix (or NULL)
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">Notes</FONT></H3>
On input, matrix R must be a sequential dense Mat, with at least as many rows
and columns as the number of active columns of V. The output satisfies
V0 = V*R (where V0 represent the input V) and V'*V = I.
<P>
If V has leading columns, then they are not modified (are assumed to be already
orthonormal) and the corresponding part of R is not referenced.
<P>
Can pass NULL if R is not required.
<P>
The method to be used for block orthogonalization can be set with
<A HREF="../BV/BVSetOrthogonalization.html#BVSetOrthogonalization">BVSetOrthogonalization</A>(). If set to GS, the computation is done column by
column with successive calls to <A HREF="../BV/BVOrthogonalizeColumn.html#BVOrthogonalizeColumn">BVOrthogonalizeColumn</A>().
<P>
If V is rank-deficient or very ill-conditioned, that is, one or more columns are
(almost) linearly dependent with respect to the rest, then the algorithm may
break down or result in larger numerical error. Linearly dependent columns are
essentially replaced by random directions, and the corresponding diagonal entry
in R is set to (nearly) zero.
<P>
<P>
<H3><FONT COLOR="#883300">See Also</FONT></H3>
<A HREF="../BV/BVOrthogonalizeColumn.html#BVOrthogonalizeColumn">BVOrthogonalizeColumn</A>(), <A HREF="../BV/BVOrthogonalizeVec.html#BVOrthogonalizeVec">BVOrthogonalizeVec</A>(), <A HREF="../BV/BVSetActiveColumns.html#BVSetActiveColumns">BVSetActiveColumns</A>(), <A HREF="../BV/BVSetOrthogonalization.html#BVSetOrthogonalization">BVSetOrthogonalization</A>(), <A HREF="../BV/BVOrthogBlockType.html#BVOrthogBlockType">BVOrthogBlockType</A>
<BR><P><B><FONT COLOR="#883300">Location: </FONT></B><A HREF="../../../src/sys/classes/bv/interface/bvorthog.c.html#BVOrthogonalize">src/sys/classes/bv/interface/bvorthog.c</A>
<BR><A HREF="./index.html">Index of all BV routines</A>
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