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<div id="version" align=right><b>slepc-3.23.1 2025-05-01</b></div>
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<H1>BVMatProject</H1>
Computes the projection of a matrix onto a subspace.
<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/BVMatProject.html#BVMatProject">BVMatProject</A>(<A HREF="../BV/BV.html#BV">BV</A> X,<A HREF="https://petsc.org/release/manualpages/Mat/Mat.html#Mat">Mat</A> A,<A HREF="../BV/BV.html#BV">BV</A> Y,<A HREF="https://petsc.org/release/manualpages/Mat/Mat.html#Mat">Mat</A> M)
</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>X </B></TD><TD> - basis vectors
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>A </B></TD><TD> - (optional) matrix to be projected
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>Y </B></TD><TD> - left basis vectors, can be equal to X
</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>M </B></TD><TD> - the resulting matrix
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">Notes</FONT></H3>
If A=NULL, then it is assumed that X already contains A*X.
<P>
This operation is similar to <A HREF="../BV/BVDot.html#BVDot">BVDot</A>(), with important differences.
The goal is to compute the matrix resulting from the orthogonal projection
of A onto the subspace spanned by the columns of X, M = X^H*A*X, or the
oblique projection onto X along Y, M = Y^H*A*X.
<P>
A difference with respect to <A HREF="../BV/BVDot.html#BVDot">BVDot</A>() is that the standard inner product
is always used, regardless of a non-standard inner product being specified
with <A HREF="../BV/BVSetMatrix.html#BVSetMatrix">BVSetMatrix</A>().
<P>
On entry, M must be a sequential dense <A HREF="https://petsc.org/release/manualpages/Mat/Mat.html#Mat">Mat</A> with dimensions ky,kx at least,
where ky (resp. kx) is the number of active columns of Y (resp. X).
Another difference with respect to <A HREF="../BV/BVDot.html#BVDot">BVDot</A>() is that all entries of M are
computed except the leading ly,lx part, where ly (resp. lx) is the
number of leading columns of Y (resp. X). Hence, the leading columns of
X and Y participate in the computation, as opposed to <A HREF="../BV/BVDot.html#BVDot">BVDot</A>().
The leading part of M is assumed to be already available from previous
computations.
<P>
In the orthogonal projection case, Y=X, some computation can be saved if
A is real symmetric (or complex Hermitian). In order to exploit this
property, the symmetry flag of A must be set with <A HREF="https://petsc.org/release/manualpages/Mat/MatSetOption.html#MatSetOption">MatSetOption</A>().
<P>
<P>
<H3><FONT COLOR="#883300">See Also</FONT></H3>
<A HREF="../BV/BVDot.html#BVDot">BVDot</A>(), <A HREF="../BV/BVSetActiveColumns.html#BVSetActiveColumns">BVSetActiveColumns</A>(), <A HREF="../BV/BVSetMatrix.html#BVSetMatrix">BVSetMatrix</A>()
<BR><P><B></B><H3><FONT COLOR="#883300">Level</FONT></H3>intermediate<BR>
<H3><FONT COLOR="#883300">Location</FONT></H3>
</B><A HREF="../../../src/sys/classes/bv/interface/bvglobal.c.html#BVMatProject">src/sys/classes/bv/interface/bvglobal.c</A>
<BR><BR><A HREF="./index.html">Index of all BV routines</A>
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