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<H2><A NAME="SECTION00086000000000000000"></A><A NAME="sec:precapply"></A>
<BR>
Subroutine apply
</H2><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
<P>
<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call p%apply(x,y,desc_a,info [,trans,work])</code>
<BR></FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
<P>
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
This routine computes <!-- MATH
$y = op(B^{-1})\, x$
-->
<IMG
WIDTH="112" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img30.png"
ALT="$y = op(B^{-1}) x$">, where <IMG
WIDTH="19" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img31.png"
ALT="$B$"> is a previously built
preconditioner, stored into <code>p</code>, and <IMG
WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img32.png"
ALT="$op$">
denotes the preconditioner itself or its transpose, according to
the value of <code>trans</code>.
Note that, when MLD2P4 is used with a Krylov solver from PSBLAS,
<code>p%apply</code> is called within the PSBLAS routine <code>psb_krylov</code>
and hence it is completely transparent to the user.
</FONT></FONT></FONT>
<P>
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Arguments</B></FONT> </FONT></FONT></FONT>
<P></P>
<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
<P>
<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><TABLE CELLPADDING=3>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>x</code> </FONT></FONT></FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(in)</code>.</FONT></FONT></FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
</FONT></FONT></FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The local part of the vector <IMG
WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img33.png"
ALT="$x$">. Note that <I>type</I> and
<I>kind_parameter</I> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</FONT></FONT></FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
<code>y</code> </FONT></FONT></FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(out)</code>.</FONT></FONT></FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
</FONT></FONT></FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The local part of the vector <IMG
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img34.png"
ALT="$y$">. Note that <I>type</I> and
<I>kind_parameter</I> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</FONT></FONT></FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
<code>desc_a</code> </FONT></FONT></FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>type(psb_desc_type), intent(in)</code>. </FONT></FONT></FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
</FONT></FONT></FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> The communication descriptor associated to the matrix to be
preconditioned.</FONT></FONT></FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
<code>info</code> </FONT></FONT></FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>integer, intent(out)</code>.</FONT></FONT></FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
</FONT></FONT></FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node25.html#sec:errors">8</A> for details.</FONT></FONT></FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
<code>trans</code> </FONT></FONT></FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <code>character(len=1), optional, intent(in).</code></FONT></FONT></FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
</FONT></FONT></FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> If <code>trans</code> = <code>'N','n'</code> then <!-- MATH
$op(B^{-1}) = B^{-1}$
-->
<IMG
WIDTH="123" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img35.png"
ALT="$op(B^{-1}) = B^{-1}$">;
if <code>trans</code> = <code>'T','t'</code> then <!-- MATH
$op(B^{-1}) = B^{-T}$
-->
<IMG
WIDTH="126" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="img36.png"
ALT="$op(B^{-1}) = B^{-T}$">
(transpose of <IMG
WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img37.png"
ALT="$B^{-1})$">; if <code>trans</code> = <code>'C','c'</code> then <!-- MATH
$op(B^{-1}) = B^{-C}$
-->
<IMG
WIDTH="126" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="img38.png"
ALT="$op(B^{-1}) = B^{-C}$">
(conjugate transpose of <IMG
WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img37.png"
ALT="$B^{-1})$">.</FONT></FONT></FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
<code>work</code> </FONT></FONT></FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> <I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), optional, target</code>.</FONT></FONT></FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
</FONT></FONT></FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"> Workspace. Its size should be at
least <code>4 * psb_cd_get_local_</code> <code>cols(desc_a)</code> (see the PSBLAS User's Guide).
Note that <I>type</I> and <I>kind_parameter</I> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</FONT></FONT></FONT></TD>
</TR>
</TABLE><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
<P>
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">For compatibility with the previous versions of MLD2P4, this routine can be also invoked
as follows:
</FONT></FONT></FONT>
<P>
<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
<DIV ALIGN="CENTER"><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><code>call mld_precaply(p,what,val,info)</code>
</FONT></FONT></FONT></DIV><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
<P>
<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
<P>
<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT><HR>
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