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<H1>IPPseudoOrthogonalize</H1>
Orthogonalize a vector with respect to two set of vectors in the sense of a pseudo-inner product.
<H3><FONT COLOR="#883300">Synopsis</FONT></H3>
<PRE>
#include "slepcip.h"
PetscErrorCode IPPseudoOrthogonalize(IP ip,PetscInt n,Vec *V,PetscReal *omega,Vec v,PetscScalar *H,PetscReal *norm,PetscBool *lindep)
</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 inner product (<A HREF="../IP/IP.html#IP">IP</A>) context
</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>V </B></TD><TD> - set of vectors
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>omega </B></TD><TD> - set of signs that define a signature matrix
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">Input/Output Parameter</FONT></H3>
<DT><B>v </B> - (input) vector to be orthogonalized and (output) result of
orthogonalization
<br>
<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
</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 is the analogue of <A HREF="../IP/IPOrthogonalize.html#IPOrthogonalize">IPOrthogonalize</A>, but for the indefinite
case. When using an indefinite <A HREF="../IP/IP.html#IP">IP</A> the norm is not well defined, so we
take the convention of having negative norms in such cases. The
orthogonalization is then defined by a set of vectors V satisfying
V'*B*V=Omega, where Omega is a signature matrix diag([+/-1,...,+/-1]).
<P>
On exit, v = v0 - V*Omega*H, where v0 is the original vector v.
<P>
This routine does not normalize the resulting vector. The output
argument 'norm' may be negative.
<P>
<P>
<H3><FONT COLOR="#883300">See Also</FONT></H3>
<A HREF="../IP/IPSetOrthogonalization.html#IPSetOrthogonalization">IPSetOrthogonalization</A>(), <A HREF="../IP/IPOrthogonalize.html#IPOrthogonalize">IPOrthogonalize</A>()
<BR><P><B><FONT COLOR="#883300">Location: </FONT></B><A HREF="../../../src/ip/ipbiorthog.c.html#IPPseudoOrthogonalize">src/ip/ipbiorthog.c</A>
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