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<H1>IPBOrthogonalize</H1>
B-Orthogonalize a vector with respect to two set of vectors.
<H3><FONT COLOR="#883300">Synopsis</FONT></H3>
<PRE>
#include "slepcip.h"
PetscErrorCode IPBOrthogonalize(IP ip,PetscInt nds,Vec *defl,Vec *BDS,PetscReal *BDSnorms,PetscInt n,PetscBool *which,Vec *V,Vec *BV,PetscReal *BVnorms,Vec v,Vec Bv,PetscScalar *H,PetscReal *norm,PetscBool *lindep)
</PRE>
Collective on <A HREF="../IP/IP.html#IP">IP</A>
<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 inner product (<A HREF="../IP/IP.html#IP">IP</A>) context
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>nds </B></TD><TD> - number of columns of defl
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>defl </B></TD><TD> - first set of vectors
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>BDS </B></TD><TD> - B * defl
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>BDSnorms </B></TD><TD> - DS_i' * B * DS_i
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>n </B></TD><TD> - number of columns of V
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>which </B></TD><TD> - logical array indicating columns of V to be used
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>V </B></TD><TD> - second set of vectors
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>BV </B></TD><TD> - B * V
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>BVnorms </B></TD><TD> - V_i' * B * V_i
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">Input/Output 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> - (input) vector to be orthogonalized and (output) result of
orthogonalization
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>Bv </B></TD><TD> - (input/output) B * v
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">Output Parameter</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>H </B></TD><TD> - coefficients computed during orthogonalization with V, of size nds+n
if norm == NULL, and nds+n+1 otherwise.
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>norm </B></TD><TD> - norm of the vector after being orthogonalized
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>lindep </B></TD><TD> - flag indicating that refinement did not improve the quality
of orthogonalization
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">Notes</FONT></H3>
This function applies an orthogonal projector to project vector v onto the
orthogonal complement of the span of the columns of defl and V.
<P>
On exit, v0 = [V v]*H, where v0 is the original vector v.
<P>
This routine does not normalize the resulting vector.
<P>
<P>
<H3><FONT COLOR="#883300">See Also</FONT></H3>
<A HREF="../IP/IPSetOrthogonalization.html#IPSetOrthogonalization">IPSetOrthogonalization</A>(), <A HREF="../IP/IPBiOrthogonalize.html#IPBiOrthogonalize">IPBiOrthogonalize</A>()
<BR><P><B><FONT COLOR="#883300">Location: </FONT></B><A HREF="../../../src/ip/ipborthog.c.html#IPBOrthogonalize">src/ip/ipborthog.c</A>
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