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<!--Converted with LaTeX2HTML 2012 (1.2)
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original version by: Nikos Drakos, CBLU, University of Leeds
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* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
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* with significant contributions from:
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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<TITLE>Subroutine apply</TITLE>
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<B> <A NAME="tex2html334"
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<!--End of Navigation Panel-->
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<H2><A NAME="SECTION00086000000000000000"></A><A NAME="sec:precapply"></A>
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<BR>
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Subroutine apply
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</H2>
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<P>
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<DIV ALIGN="CENTER">
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<code>call p%apply(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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$y = op(B^{-1})\, x$
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-->
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<IMG
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WIDTH="112" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img29.png"
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ALT="$y = op(B^{-1}) x$">, where <IMG
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WIDTH="19" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img30.png"
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ALT="$B$"> is a previously built
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preconditioner, stored into <code>p</code>, and <IMG
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WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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SRC="img31.png"
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ALT="$op$">
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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>p%apply</code> is called within the PSBLAS routine <code>psb_krylov</code>
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and hence it is completely transparent to the user.
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<P>
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<FONT SIZE="+1"><B>Arguments</B></FONT>
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<P></P>
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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>x</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><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 <IMG
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WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
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SRC="img32.png"
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ALT="$x$">. Note that <I>type</I> and
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<I>kind_parameter</I> 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><I>type</I><code>(</code><I>kind_parameter</I><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 <IMG
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WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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SRC="img33.png"
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ALT="$y$">. Note that <I>type</I> and
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<I>kind_parameter</I> 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="node25.html#sec:errors">8</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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$op(B^{-1}) = B^{-1}$
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-->
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<IMG
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WIDTH="123" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img34.png"
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ALT="$op(B^{-1}) = B^{-1}$">;
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if <code>trans</code> = <code>'T','t'</code> then <!-- MATH
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$op(B^{-1}) = B^{-T}$
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-->
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<IMG
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WIDTH="126" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
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SRC="img35.png"
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ALT="$op(B^{-1}) = B^{-T}$">
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(transpose of <IMG
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WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img36.png"
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ALT="$B^{-1})$">; if <code>trans</code> = <code>'C','c'</code> then <!-- MATH
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$op(B^{-1}) = B^{-C}$
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-->
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<IMG
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WIDTH="126" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
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SRC="img37.png"
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ALT="$op(B^{-1}) = B^{-C}$">
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(conjugate transpose of <IMG
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WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img36.png"
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ALT="$B^{-1})$">.</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><I>type</I><code>(</code><I>kind_parameter</I><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 <I>type</I> and <I>kind_parameter</I> 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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For compatibility with the previous versions of MLD2P4, this routine can be also invoked
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as follows:
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<P>
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<DIV ALIGN="CENTER">
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<code>call mld_precaply(p,what,val,info)</code>
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</DIV>
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<P>
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