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<div id="version" align=right><b>slepc-3.23.1 2025-05-01</b></div>
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<H1>BVOrthogonalizeColumn</H1>
Orthogonalize one of the column vectors with respect to the previous ones.
<H3><FONT COLOR="#883300">Synopsis</FONT></H3>
<PRE>
#include "slepcbv.h"
<A HREF="https://petsc.org/release/manualpages/Sys/PetscErrorCode.html#PetscErrorCode">PetscErrorCode</A> <A HREF="../BV/BVOrthogonalizeColumn.html#BVOrthogonalizeColumn">BVOrthogonalizeColumn</A>(<A HREF="../BV/BV.html#BV">BV</A> bv,<A HREF="https://petsc.org/release/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</A> j,<A HREF="https://petsc.org/release/manualpages/Sys/PetscScalar.html#PetscScalar">PetscScalar</A> *H,<A HREF="https://petsc.org/release/manualpages/Sys/PetscReal.html#PetscReal">PetscReal</A> *norm,<A HREF="https://petsc.org/release/manualpages/Sys/PetscBool.html#PetscBool">PetscBool</A> *lindep)
</PRE>
Collective
<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>bv </B></TD><TD> - the basis vectors context
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>j </B></TD><TD> - index of column to be orthogonalized
</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>H </B></TD><TD> - (optional) coefficients computed during orthogonalization
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>norm </B></TD><TD> - (optional) norm of the vector after being orthogonalized
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>lindep </B></TD><TD> - (optional) 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[j] onto
the orthogonal complement of the span of the columns V[0..j-1],
where V[.] are the vectors of <A HREF="../BV/BV.html#BV">BV</A>. The columns V[0..j-1] are assumed to be
mutually orthonormal.
<P>
Leading columns V[0..l-1] also participate in the orthogonalization, as well
as the constraints. If H is given, it must have enough space to store
j-l+1 coefficients (the last coefficient will contain the value norm, unless
the norm argument is NULL).
<P>
If a non-standard inner product has been specified with <A HREF="../BV/BVSetMatrix.html#BVSetMatrix">BVSetMatrix</A>(),
then the vector is B-orthogonalized, using the non-standard inner product
defined by matrix B. The output vector satisfies V[j]'*B*V[0..j-1] = 0.
<P>
This routine does not normalize the resulting vector, see <A HREF="../BV/BVOrthonormalizeColumn.html#BVOrthonormalizeColumn">BVOrthonormalizeColumn</A>().
<P>
In the case of an indefinite inner product, the lindep parameter is not
computed (set to false).
<P>
<P>
<H3><FONT COLOR="#883300">See Also</FONT></H3>
<A HREF="../BV/BVSetOrthogonalization.html#BVSetOrthogonalization">BVSetOrthogonalization</A>(), <A HREF="../BV/BVSetMatrix.html#BVSetMatrix">BVSetMatrix</A>(), <A HREF="../BV/BVSetActiveColumns.html#BVSetActiveColumns">BVSetActiveColumns</A>(), <A HREF="../BV/BVOrthogonalize.html#BVOrthogonalize">BVOrthogonalize</A>(), <A HREF="../BV/BVOrthogonalizeVec.html#BVOrthogonalizeVec">BVOrthogonalizeVec</A>(), <A HREF="../BV/BVGetNumConstraints.html#BVGetNumConstraints">BVGetNumConstraints</A>(), <A HREF="../BV/BVOrthonormalizeColumn.html#BVOrthonormalizeColumn">BVOrthonormalizeColumn</A>()
<BR><P><B></B><H3><FONT COLOR="#883300">Level</FONT></H3>advanced<BR>
<H3><FONT COLOR="#883300">Location</FONT></H3>
</B><A HREF="../../../src/sys/classes/bv/interface/bvorthog.c.html#BVOrthogonalizeColumn">src/sys/classes/bv/interface/bvorthog.c</A>
<BR><BR><A HREF="./index.html">Index of all BV routines</A>
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