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<!--Converted with LaTeX2HTML 2002-2-1 (1.71)
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<H2><A NAME="SECTION00084000000000000000"></A><A NAME="sec:precaply"></A>
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<BR>
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Subroutine mld_precaply
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</H2>
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<P>
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<DIV ALIGN="CENTER">
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<code>mld_precaply(p,x,y,desc_a,info)</code>
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<BR><code>mld_precaply(p,x,y,desc_a,info,trans,work)</code>
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<BR>
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</DIV>
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<P>
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This routine computes <!-- MATH
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$y = op(M^{-1})\, x$
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-->
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<SPAN CLASS="MATH"><IMG
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WIDTH="118" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img94.png"
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ALT="$y = op(M^{-1}) x$"></SPAN>, where <SPAN CLASS="MATH"><IMG
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WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img59.png"
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ALT="$M$"></SPAN> is a previously built
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preconditioner, stored into <code>p</code>, and <SPAN CLASS="MATH"><IMG
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WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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SRC="img95.png"
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ALT="$op$"></SPAN>
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denotes the preconditioner itself or its transpose, according to
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the value of <code>trans</code>.
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Note that, when MLD2P4 is used with a Krylov solver from PSBLAS,
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<code>mld_precaply</code> is called within the PSBLAS routine <code>mld_krylov</code>
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and hence it is completely transparent to the user.
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<P>
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<BIG CLASS="LARGE"><B>Arguments</B></BIG>
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<P>
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<TABLE CELLPADDING=3>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><SPAN CLASS="textit">x</SPAN><code>prec_type), intent(inout)</code>.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure, containing the local part of <SPAN CLASS="MATH"><IMG
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WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img59.png"
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ALT="$M$"></SPAN>.
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Note that <SPAN CLASS="textit">x</SPAN> must be chosen according
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to the real/complex, single/double precision version of MLD2P4 under use.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>x</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><SPAN CLASS="textit">type</SPAN><code>(</code><SPAN CLASS="textit">kind_parameter</SPAN><code>), dimension(:), intent(in)</code>.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <SPAN CLASS="MATH"><IMG
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WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img96.png"
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ALT="$x$"></SPAN>. Note that <SPAN CLASS="textit">type</SPAN> and
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<SPAN CLASS="textit">kind_parameter</SPAN> must be chosen according
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to the real/complex, single/double precision version of MLD2P4 under use.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>y</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><SPAN CLASS="textit">type</SPAN><code>(</code><SPAN CLASS="textit">kind_parameter</SPAN><code>), dimension(:), intent(out)</code>.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <SPAN CLASS="MATH"><IMG
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WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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SRC="img97.png"
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ALT="$y$"></SPAN>. Note that <SPAN CLASS="textit">type</SPAN> and
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<SPAN CLASS="textit">kind_parameter</SPAN> must be chosen according
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to the real/complex, single/double precision version of MLD2P4 under use.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>desc_a</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_desc_type), intent(in)</code>.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The communication descriptor associated to the matrix to be
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preconditioned.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section <A HREF="node22.html#sec:errors">7</A> for details.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>trans</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>character(len=1), optional, intent(in).</code></TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>If <code>trans</code> = <code>'N','n'</code> then <!-- MATH
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$op(M^{-1}) = M^{-1}$
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-->
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<SPAN CLASS="MATH"><IMG
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WIDTH="132" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img98.png"
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ALT="$op(M^{-1}) = M^{-1}$"></SPAN>;
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if <code>trans</code> = <code>'T','t'</code> then <!-- MATH
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$op(M^{-1}) = M^{-T}$
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-->
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<SPAN CLASS="MATH"><IMG
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WIDTH="135" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
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SRC="img99.png"
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ALT="$op(M^{-1}) = M^{-T}$"></SPAN>
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(transpose of <SPAN CLASS="MATH"><IMG
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WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img100.png"
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ALT="$M^{-1})$"></SPAN>; if <code>trans</code> = <code>'C','c'</code> then <!-- MATH
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$op(M^{-1}) = M^{-C}$
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-->
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<SPAN CLASS="MATH"><IMG
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WIDTH="136" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
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SRC="img101.png"
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ALT="$op(M^{-1}) = M^{-C}$"></SPAN>
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(conjugate transpose of <SPAN CLASS="MATH"><IMG
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WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img100.png"
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ALT="$M^{-1})$"></SPAN>.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>work</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><SPAN CLASS="textit">type</SPAN><code>(</code><SPAN CLASS="textit">kind_parameter</SPAN><code>), dimension(:), optional, target</code>.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Workspace. Its size should be at
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least <code>4 * psb_cd_get_local_</code> <code>cols(desc_a)</code> (see the PSBLAS User's Guide).
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Note that <SPAN CLASS="textit">type</SPAN> and <SPAN CLASS="textit">kind_parameter</SPAN> must be chosen according
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to the real/complex, single/double precision version of MLD2P4 under use.</TD>
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</TR>
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</TABLE>
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<P>
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<P>
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<ADDRESS>
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Salvatore Filippone
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2008-07-23
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