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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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<H2><A NAME="SECTION00086000000000000000"></A><A NAME="sec:precapply"></A>
<BR>
Method apply
</H2><BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
<P>
<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
<DIV ALIGN="CENTER"><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"><code>call p%apply(x,y,desc_a,info [,trans,work])</code>
<BR></BIG></BIG></BIG></DIV><BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
<P>
<BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
This method computes <!-- MATH
$y = op(B^{-1})\, x$
-->
<SPAN CLASS="MATH"><IMG
WIDTH="113" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img86.png"
ALT="$y = op(B^{-1})\, x$"></SPAN>, where <SPAN CLASS="MATH"><IMG
WIDTH="19" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img24.png"
ALT="$B$"></SPAN> is a previously built
preconditioner, stored into <code>p</code>, and <SPAN CLASS="MATH"><IMG
WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img87.png"
ALT="$op$"></SPAN>
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 method <code>psb_krylov</code>
and hence it is completely transparent to the user.
</BIG></BIG></BIG>
<P>
<BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"><B>Arguments</B></BIG> </BIG></BIG></BIG>
<P></P>
<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
<P>
<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG><TABLE CELLPADDING=3>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
<code>x</code> </BIG></BIG></BIG></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"> <SPAN CLASS="textit">type</SPAN><code>(</code><SPAN CLASS="textit">kind_parameter</SPAN><code>), dimension(:), intent(in)</code>.</BIG></BIG></BIG></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
</BIG></BIG></BIG></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"> The local part of the vector <SPAN CLASS="MATH"><IMG
WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img88.png"
ALT="$x$"></SPAN>. Note that <SPAN CLASS="textit">type</SPAN> and
<SPAN CLASS="textit">kind_parameter</SPAN> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</BIG></BIG></BIG></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
<code>y</code> </BIG></BIG></BIG></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"> <SPAN CLASS="textit">type</SPAN><code>(</code><SPAN CLASS="textit">kind_parameter</SPAN><code>), dimension(:), intent(out)</code>.</BIG></BIG></BIG></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
</BIG></BIG></BIG></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"> The local part of the vector <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img89.png"
ALT="$y$"></SPAN>. Note that <SPAN CLASS="textit">type</SPAN> and
<SPAN CLASS="textit">kind_parameter</SPAN> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</BIG></BIG></BIG></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
<code>desc_a</code> </BIG></BIG></BIG></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"> <code>type(psb_desc_type), intent(in)</code>. </BIG></BIG></BIG></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
</BIG></BIG></BIG></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"> The communication descriptor associated to the matrix to be
preconditioned.</BIG></BIG></BIG></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
<code>info</code> </BIG></BIG></BIG></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"> <code>integer, intent(out)</code>.</BIG></BIG></BIG></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
</BIG></BIG></BIG></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"> Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node34.html#sec:errors">8</A> for details.</BIG></BIG></BIG></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
<code>trans</code> </BIG></BIG></BIG></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"> <code>character(len=1), optional, intent(in).</code></BIG></BIG></BIG></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
</BIG></BIG></BIG></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"> If <code>trans</code> = <code>'N','n'</code> then <!-- MATH
$op(B^{-1}) = B^{-1}$
-->
<SPAN CLASS="MATH"><IMG
WIDTH="123" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img90.png"
ALT="$op(B^{-1}) = B^{-1}$"></SPAN>;
if <code>trans</code> = <code>'T','t'</code> then <!-- MATH
$op(B^{-1}) = B^{-T}$
-->
<SPAN CLASS="MATH"><IMG
WIDTH="126" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="img91.png"
ALT="$op(B^{-1}) = B^{-T}$"></SPAN>
(transpose of <SPAN CLASS="MATH"><IMG
WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img92.png"
ALT="$B^{-1})$"></SPAN>; if <code>trans</code> = <code>'C','c'</code> then <!-- MATH
$op(B^{-1}) = B^{-C}$
-->
<SPAN CLASS="MATH"><IMG
WIDTH="126" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="img93.png"
ALT="$op(B^{-1}) = B^{-C}$"></SPAN>
(conjugate transpose of <SPAN CLASS="MATH"><IMG
WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img92.png"
ALT="$B^{-1})$"></SPAN>.</BIG></BIG></BIG></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
<code>work</code> </BIG></BIG></BIG></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"> <SPAN CLASS="textit">type</SPAN><code>(</code><SPAN CLASS="textit">kind_parameter</SPAN><code>), dimension(:), optional, target</code>.</BIG></BIG></BIG></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">
</BIG></BIG></BIG></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"> 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 <SPAN CLASS="textit">type</SPAN> and <SPAN CLASS="textit">kind_parameter</SPAN> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</BIG></BIG></BIG></TD>
</TR>
</TABLE><BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
<P>
<BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">For compatibility with the previous versions of MLD2P4, this method can be also invoked
as follows:
</BIG></BIG></BIG>
<P>
<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
<DIV ALIGN="CENTER"><BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"><code>call mld_precaply(p,what,val,info)</code>
</BIG></BIG></BIG></DIV><BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
<P>
<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
<P>
<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
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