mld2p4:

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2026-10-06 22:55:12 +00:00 · 2008-07-24 13:00:39 +00:00
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33 changed files with 4592 additions and 4544 deletions
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
  Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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-<TITLE>Subroutine mld_precfree</TITLE>
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+<TITLE>Subroutine mld_precaply</TITLE>
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@@ -20,54 +20,73 @@ original version by:  Nikos Drakos, CBLU, University of Leeds

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-<H2><A NAME="SECTION00085000000000000000"></A><A NAME="sec:precfree"></A>
+<H2><A NAME="SECTION00084000000000000000"></A><A NAME="sec:precaply"></A>
 <BR>
-Subroutine mld_precfree
+Subroutine mld_precaply
 </H2>

 <P>
 <DIV ALIGN="CENTER">
-<code>mld_precfree(p,info)</code>
+<code>mld_precaply(p,x,y,desc_a,info)</code>
+<BR><code>mld_precaply(p,x,y,desc_a,info,trans,work)</code>
 <BR>
 </DIV>

 <P>
-This routine deallocates the preconditioner data structure.
+This routine computes <!-- MATH
+ $y = op(M^{-1})\, x$
+ -->
+<IMG
+ WIDTH="118" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img94.png"
+ ALT="$y = op(M^{-1})  x$">, where <IMG
+ WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
+ SRC="img59.png"
+ ALT="$M$"> is a previously built
+preconditioner, stored into <code>p</code>, and <IMG
+ WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img95.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>mld_precaply</code> is called within the PSBLAS routine <code>mld_krylov</code>
+and hence it is completely transparent to the user.

 <P>
 <FONT SIZE="+1"><B>Arguments</B></FONT>
@@ -75,24 +94,126 @@ This routine deallocates the preconditioner data structure.
 <P>
 <TABLE CELLPADDING=3>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298>The preconditioner data structure. Note that <I>x</I> must be chosen according
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure, containing the local part of <IMG
+ WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
+ SRC="img59.png"
+ ALT="$M$">.
+                Note that <I>x</I> must be chosen according
                to the real/complex, single/double precision version of MLD2P4 under use.</TD>
 </TR>
-<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><code>integer, intent(out)</code>.</TD>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>x</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(in)</code>.</TD>
 </TR>
 <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
-<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node22.html#sec:errors">7</A> for details.</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG
+ WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img96.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.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>y</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(out)</code>.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG
+ WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img97.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.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>desc_a</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_desc_type), intent(in)</code>.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The communication descriptor associated to the matrix to be
+                preconditioned.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node23.html#sec:errors">7</A> for details.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>trans</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>character(len=1), optional, intent(in).</code></TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>If <code>trans</code> = <code>'N','n'</code> then <!-- MATH
+ $op(M^{-1}) = M^{-1}$
+ -->
+<IMG
+ WIDTH="132" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img98.png"
+ ALT="$op(M^{-1}) = M^{-1}$">;
+                if <code>trans</code> = <code>'T','t'</code> then <!-- MATH
+ $op(M^{-1}) = M^{-T}$
+ -->
+<IMG
+ WIDTH="135" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
+ SRC="img99.png"
+ ALT="$op(M^{-1}) = M^{-T}$">
+                (transpose of <IMG
+ WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img100.png"
+ ALT="$M^{-1})$">;  if <code>trans</code> = <code>'C','c'</code> then <!-- MATH
+ $op(M^{-1}) = M^{-C}$
+ -->
+<IMG
+ WIDTH="136" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
+ SRC="img101.png"
+ ALT="$op(M^{-1}) = M^{-C}$">
+                (conjugate transpose of <IMG
+ WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
+ SRC="img100.png"
+ ALT="$M^{-1})$">.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>work</code></TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), optional, target</code>.</TD>
+</TR>
+<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
+<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>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.</TD>
 </TR>
 </TABLE>

 <P>

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