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<div id="version" align=right><b>petsc-3.10.3 2018-12-18</b></div>
<div id="bugreport" align=right><a href="mailto:petsc-maint@mcs.anl.gov?subject=Typo or Error in Documentation &body=Please describe the typo or error in the documentation: petsc-3.10.3 v3.10.3 docs/manualpages/Mat/MatForwardSolve.html "><small>Report Typos and Errors</small></a></div>
<A NAME="MatForwardSolve"><H1>MatForwardSolve</H1></A>
Solves L x = b, given a factored matrix, A = LU, or U^T*D^(1/2) x = b, given a factored symmetric matrix, A = U^T*D*U,
<H3><FONT COLOR="#CC3333">Synopsis</FONT></H3>
<PRE>
#include "petscmat.h"
<A HREF="../Sys/PetscErrorCode.html#PetscErrorCode">PetscErrorCode</A> <A HREF="../Mat/MatForwardSolve.html#MatForwardSolve">MatForwardSolve</A>(<A HREF="../Mat/Mat.html#Mat">Mat</A> mat,<A HREF="../Vec/Vec.html#Vec">Vec</A> b,<A HREF="../Vec/Vec.html#Vec">Vec</A> x)
</PRE>
Neighbor-wise Collective on <A HREF="../Mat/Mat.html#Mat">Mat</A> and <A HREF="../Vec/Vec.html#Vec">Vec</A>
<P>
<H3><FONT COLOR="#CC3333">Input Parameters</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>mat </B></TD><TD>- the factored matrix
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>b </B></TD><TD>- the right-hand-side vector
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#CC3333">Output Parameter</FONT></H3>
<DT><B>x </B> -the result vector
<br>
<P>
<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
<A HREF="../Mat/MatSolve.html#MatSolve">MatSolve</A>() should be used for most applications, as it performs
a forward solve followed by a backward solve.
<P>
The vectors b and x cannot be the same, i.e., one cannot
call <A HREF="../Mat/MatForwardSolve.html#MatForwardSolve">MatForwardSolve</A>(A,x,x).
<P>
For matrix in seqsbaij format with block size larger than 1,
the diagonal blocks are not implemented as D = D^(1/2) * D^(1/2) yet.
<A HREF="../Mat/MatForwardSolve.html#MatForwardSolve">MatForwardSolve</A>() solves U^T*D y = b, and
<A HREF="../Mat/MatBackwardSolve.html#MatBackwardSolve">MatBackwardSolve</A>() solves U x = y.
Thus they do not provide a symmetric preconditioner.
<P>
Most users should employ the simplified <A HREF="../KSP/KSP.html#KSP">KSP</A> interface for linear solvers
instead of working directly with matrix algebra routines such as this.
See, e.g., <A HREF="../KSP/KSPCreate.html#KSPCreate">KSPCreate</A>().
<P>
<P>
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../Mat/MatSolve.html#MatSolve">MatSolve</A>(), <A HREF="../Mat/MatBackwardSolve.html#MatBackwardSolve">MatBackwardSolve</A>()
<BR><P><B></B><H3><FONT COLOR="#CC3333">Level</FONT></H3>developer<BR>
<H3><FONT COLOR="#CC3333">Location</FONT></H3>
</B><A HREF="../../../src/mat/interface/matrix.c.html#MatForwardSolve">src/mat/interface/matrix.c</A>
<P><H3><FONT COLOR="CC3333">Implementations</FONT></H3><A HREF="../../../src/mat/impls/baij/seq/baijsolvnat.c.html#MatForwardSolve_SeqBAIJ_3_NaturalOrdering">MatForwardSolve_SeqBAIJ_3_NaturalOrdering in src/mat/impls/baij/seq/baijsolvnat.c</A><BR>
<A HREF="../../../src/mat/impls/baij/seq/baijsolvnat.c.html#MatForwardSolve_SeqBAIJ_2_NaturalOrdering">MatForwardSolve_SeqBAIJ_2_NaturalOrdering in src/mat/impls/baij/seq/baijsolvnat.c</A><BR>
<A HREF="../../../src/mat/impls/baij/seq/baijsolvnat.c.html#MatForwardSolve_SeqBAIJ_1_NaturalOrdering">MatForwardSolve_SeqBAIJ_1_NaturalOrdering in src/mat/impls/baij/seq/baijsolvnat.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_N_inplace">MatForwardSolve_SeqSBAIJ_N_inplace in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_N_NaturalOrdering">MatForwardSolve_SeqSBAIJ_N_NaturalOrdering in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_N_NaturalOrdering_inplace">MatForwardSolve_SeqSBAIJ_N_NaturalOrdering_inplace in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_7_NaturalOrdering">MatForwardSolve_SeqSBAIJ_7_NaturalOrdering in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_7_NaturalOrdering_inplace">MatForwardSolve_SeqSBAIJ_7_NaturalOrdering_inplace in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_6_NaturalOrdering">MatForwardSolve_SeqSBAIJ_6_NaturalOrdering in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_6_NaturalOrdering_inplace">MatForwardSolve_SeqSBAIJ_6_NaturalOrdering_inplace in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_5_NaturalOrdering">MatForwardSolve_SeqSBAIJ_5_NaturalOrdering in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_5_NaturalOrdering_inplace">MatForwardSolve_SeqSBAIJ_5_NaturalOrdering_inplace in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_4_NaturalOrdering">MatForwardSolve_SeqSBAIJ_4_NaturalOrdering in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace">MatForwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_3_NaturalOrdering">MatForwardSolve_SeqSBAIJ_3_NaturalOrdering in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace">MatForwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_2_NaturalOrdering">MatForwardSolve_SeqSBAIJ_2_NaturalOrdering in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_2_NaturalOrdering_inplace">MatForwardSolve_SeqSBAIJ_2_NaturalOrdering_inplace in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_1">MatForwardSolve_SeqSBAIJ_1 in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_1_inplace">MatForwardSolve_SeqSBAIJ_1_inplace in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_1_NaturalOrdering">MatForwardSolve_SeqSBAIJ_1_NaturalOrdering in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
<A HREF="../../../src/mat/impls/sbaij/seq/sbaijfact2.c.html#MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace">MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace in src/mat/impls/sbaij/seq/sbaijfact2.c</A><BR>
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