fix documentation bug for NRM2
This commit is contained in:
Salvatore Filippone
2010-06-22 12:42:39 +00:00
parent 591166264b
commit e4452fe0a6
214 changed files with 8663 additions and 8784 deletions
+602 -108
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@@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
<HTML>
<HEAD>
<TITLE>psb_gather -- Gather Global Dense Matrix</TITLE>
<META NAME="description" CONTENT="psb_gather -- Gather Global Dense Matrix">
<TITLE>psb_ovrl -- Overlap Update</TITLE>
<META NAME="description" CONTENT="psb_ovrl -- Overlap Update">
<META NAME="keywords" CONTENT="userhtml">
<META NAME="resource-type" CONTENT="document">
<META NAME="distribution" CONTENT="global">
@@ -20,123 +20,112 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<H2><A NAME="SECTION00063000000000000000">
psb_gather -- Gather Global Dense Matrix</A>
<H2><A NAME="SECTION00062000000000000000">
psb_ovrl -- Overlap Update</A>
</H2>
<P>
These subroutines collect the portions of global dense matrix
distributed over all process into one single array stored on one
process.
These subroutines applies an overlap operator to the input vector:
<P>
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{displaymath}
glob\_x \leftarrow collect(loc\_x_i)
x \leftarrow Q x
\end{displaymath}
-->
<IMG
WIDTH="163" HEIGHT="28" BORDER="0"
SRC="img75.png"
ALT="\begin{displaymath}glob\_x \leftarrow collect(loc\_x_i) \end{displaymath}">
WIDTH="55" HEIGHT="27" BORDER="0"
SRC="img65.png"
ALT="\begin{displaymath}x \leftarrow Q x \end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
where:
<DL>
<DT><STRONG><IMG
WIDTH="46" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img76.png"
ALT="$glob\_x$"></STRONG></DT>
<DD>is the global submatrix <!-- MATH
$glob\_x_{1:m,1:n}$
-->
<IMG
WIDTH="91" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img77.png"
ALT="$glob\_x_{1:m,1:n}$">
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img26.png"
ALT="$x$"></STRONG></DT>
<DD>is the global dense submatrix <IMG
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img26.png"
ALT="$x$">
</DD>
<DT><STRONG><IMG
WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img78.png"
ALT="$loc\_x_i$"></STRONG></DT>
<DD>is the local portion of global dense matrix on
process <IMG
WIDTH="9" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img4.png"
ALT="$i$">.
</DD>
<DT><STRONG><IMG
WIDTH="49" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img79.png"
ALT="$collect$"></STRONG></DT>
<DD>is the collect function.
WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img66.png"
ALT="$Q$"></STRONG></DT>
<DD>is the overlap operator; it is the composition of two
operators <IMG
WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img67.png"
ALT="$ P_a$"> and <IMG
WIDTH="27" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
SRC="img68.png"
ALT="$ P^{T}$">.
</DD>
</DL>
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="2681"></A>
<DIV ALIGN="CENTER"><A NAME="2665"></A>
<TABLE>
<CAPTION><STRONG>Table 15:</STRONG>
<CAPTION><STRONG>Table 14:</STRONG>
Data types</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><IMG
WIDTH="33" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img80.png"
ALT="$x_i, y$"></TD>
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img26.png"
ALT="$x$"></TD>
<TD ALIGN="LEFT"><B>Subroutine</B></TD>
</TR>
<TR><TD ALIGN="LEFT">Integer</TD>
<TD ALIGN="LEFT">psb_gather</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">psb_gather</TD>
<TD ALIGN="LEFT">psb_ovrl</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">psb_gather</TD>
<TD ALIGN="LEFT">psb_ovrl</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Complex</TD>
<TD ALIGN="LEFT">psb_gather</TD>
<TD ALIGN="LEFT">psb_ovrl</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Complex</TD>
<TD ALIGN="LEFT">psb_gather</TD>
<TD ALIGN="LEFT">psb_ovrl</TD>
</TR>
</TABLE>
</DIV>
@@ -147,9 +136,9 @@ Data types</CAPTION>
<P>
<PRE>
call psb_gather(glob_x, loc_x, desc_a, info, root)
call psb_gather(glob_x, loc_x, desc_a, info, root)
</PRE>
call psb_ovrl(x, desc_a, info)
call psb_ovrl(x, desc_a, info, update=update_type, work=work)
</PRE>
<P>
<DL>
@@ -159,21 +148,21 @@ call psb_gather(glob_x, loc_x, desc_a, info, root)
<DT><STRONG><B>On Entry</B></STRONG></DT>
<DD>
</DD>
<DT><STRONG>loc_x</STRONG></DT>
<DD>the local portion of global dense matrix
<IMG
WIDTH="46" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img76.png"
ALT="$glob\_x$">.
<DT><STRONG>x</STRONG></DT>
<DD>global dense matrix <IMG
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img26.png"
ALT="$x$">.
<BR>
Scope: <B>local</B>
<BR>
Type: <B>required</B>
Type: <B>required</B>
<BR>
Intent: <B>in</B>.
Intent: <B>inout</B>.
<BR>
Specified as: a rank one or two array containing numbers of the type
indicated in Table&nbsp;<A HREF="#tab:gather">15</A>.
Specified as: a rank one or two array
containing numbers of type specified in
Table&nbsp;<A HREF="#tab:f90ovrl">14</A>.
</DD>
<DT><STRONG>desc_a</STRONG></DT>
<DD>contains data structures for communications.
@@ -186,43 +175,75 @@ Intent: <B>in</B>.
<BR>
Specified as: a structured data of type descdata<TT>psb_desc_type</TT>.
</DD>
<DT><STRONG>root</STRONG></DT>
<DD>The process that holds the global copy. If <IMG
WIDTH="75" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img81.png"
ALT="$root=-1$"> all
the processes will have a copy of the global vector.
<BR>
<DT><STRONG>update</STRONG></DT>
<DD>Update operator.
<BR><DL>
<DT><STRONG>update = psb_none_</STRONG></DT>
<DD>Do nothing;
</DD>
<DT><STRONG>update = psb_add_</STRONG></DT>
<DD>Sum overlap entries, i.e. apply <IMG
WIDTH="26" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
SRC="img69.png"
ALT="$P^T$">;
</DD>
<DT><STRONG>update = psb_avg_</STRONG></DT>
<DD>Average overlap entries, i.e. apply <IMG
WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
SRC="img70.png"
ALT="$P_aP^T$">;
</DD>
</DL>
Scope: <B>global</B>
<BR>
Type: <B>optional</B>
<BR>
Intent: <B>in</B>.
<BR>
Specified as: an integer variable <!-- MATH
$-1\le root\le np-1$
Default: <!-- MATH
$update\_type = psb\_avg\_$
-->
<IMG
WIDTH="140" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img82.png"
ALT="$-1\le root\le np-1$">, default <IMG
WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img83.png"
ALT="$-1$">.
WIDTH="166" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img71.png"
ALT="$update\_type = psb\_avg\_ $">
<BR>
Scope: <B>global</B>
<BR>
Specified as: a integer variable.
</DD>
<DT><STRONG>work</STRONG></DT>
<DD>the work array.
<BR>
Scope: <B>local</B>
<BR>
Type: <B>optional</B>
<BR>
Intent: <B>inout</B>.
<BR>
Specified as: a one dimensional array of the same type of <IMG
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img26.png"
ALT="$x$">.
<P>
</DD>
<DT><STRONG><B>On Return</B></STRONG></DT>
<DD>
</DD>
<DT><STRONG>glob_x</STRONG></DT>
<DD>The array where the local parts must be gathered.
<DT><STRONG>x</STRONG></DT>
<DD>global dense result matrix <IMG
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img26.png"
ALT="$x$">.
<BR>
Scope: <B>global</B>
Scope: <B>local</B>
<BR>
Type: <B>required</B>
Type: <B>required</B>
<BR>
Intent: <B>out</B>.
Intent: <B>inout</B>.
<BR>
Specified as: a rank one or two array.
Specified as: an array of rank one or two
containing numbers of type specified in
Table&nbsp;<A HREF="#tab:f90ovrl">14</A>.
</DD>
<DT><STRONG>info</STRONG></DT>
<DD>Error code.
@@ -237,29 +258,502 @@ An integer value; 0 means no error has been detected.
</DD>
</DL>
<P>
<FONT SIZE="+1"><B>Notes</B></FONT>
<OL>
<LI>If there is no overlap in the data distribution associated with
the descriptor, no operations are performed;
</LI>
<LI>The operator <IMG
WIDTH="27" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
SRC="img68.png"
ALT="$ P^{T}$"> performs the reduction sum of overlap
elements; it is a ``prolongation'' operator <IMG
WIDTH="26" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
SRC="img69.png"
ALT="$P^T$"> that
replicates overlap elements, accounting for the physical replication
of data;
</LI>
<LI>The operator <IMG
WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img67.png"
ALT="$ P_a$"> performs a scaling on the overlap elements by
the amount of replication; thus, when combined with the reduction
operator, it implements the average of replicated elements over all of
their instances.
</LI>
</OL>
<P>
<DIV ALIGN="CENTER"><A NAME="fig:try8x8_ov"></A><A NAME="2667"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 7:</STRONG>
Sample discretization mesh.</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<IMG
WIDTH="533" HEIGHT="453" ALIGN="BOTTOM" BORDER="0"
SRC="img73.png"
ALT="\includegraphics[scale=0.65]{figures/try8x8_ov.eps}">
<!-- MATH
$\rotatebox{-90}{\includegraphics[scale=0.65]{figures/try8x8_ov}}$
-->
<IMG
WIDTH="76" HEIGHT="2" ALIGN="BOTTOM" BORDER="0"
SRC="img72.png"
ALT="\rotatebox{-90}{\includegraphics[scale=0.65]{figures/try8x8_ov}}">
</DIV></TD></TR>
</TABLE>
</DIV>
<FONT SIZE="+1"><B>Example of use</B></FONT>
Consider the discretization mesh depicted in fig.&nbsp;<A HREF="#fig:try8x8_ov">7</A>,
partitioned among two processes as shown by the dashed lines, with an
overlap of 1 extra layer with respect to the partition of
fig.&nbsp;<A HREF="node39.html#fig:try8x8">6</A>; the data
distribution is such that each process will own 40 entries in the
index space, with an overlap of 16 entries placed at local indices 25
through 40; the halo will run from local index 41 through local index 48.. If process 0 assigns an initial value of 1 to its entries
in the <IMG
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img26.png"
ALT="$x$"> vector, and process 1 assigns a value of 2, then after a
call to <code>psb_ovrl</code> with <code>psb_avg_</code> and a call to
<code>psb_halo_</code> the contents of the local vectors will be the
following (showing a transition among the two subdomains)
<P>
<BR>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 ALIGN="CENTER">
<TR><TD ALIGN="CENTER" COLSPAN=3><FONT SIZE="-1">
Process 0</FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="CENTER" COLSPAN=3><FONT SIZE="-1">
Process 1</FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
I </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> GLOB(I) </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> X(I) </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> I </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> GLOB(I) </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> X(I) </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
1 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 1 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 33 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
2 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 2 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 34 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
3 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 3 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 3 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 35 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
4 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 4 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 4 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 36 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
5 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 5 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 5 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 37 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
6 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 6 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 6 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 38 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
7 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 7 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 7 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 39 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
8 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 8 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 8 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 40 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
9 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 9 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 9 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 41 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
10 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 10 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 10 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 42 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
11 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 11 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 11 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 43 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
12 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 12 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 12 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 44 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
13 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 13 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 13 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 45 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
14 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 14 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 14 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 46 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
15 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 15 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 15 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 47 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
16 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 16 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 16 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 48 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
17 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 17 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 17 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 49 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
18 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 18 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 18 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 50 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
19 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 19 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 19 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 51 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
20 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 20 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 20 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 52 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
21 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 21 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 21 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 53 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
22 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 22 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 22 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 54 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
23 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 23 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 23 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 55 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
24 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 24 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 24 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 56 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
25 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 25 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 25 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 57 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
26 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 26 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 26 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 58 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
27 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 27 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 27 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 59 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
28 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 28 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 28 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 60 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
29 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 29 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 29 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 61 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
30 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 30 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 30 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 62 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
31 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 31 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 31 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 63 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
32 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 32 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 32 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 64 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
33 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 33 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 33 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 25 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
34 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 34 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 34 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 26 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
35 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 35 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 35 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 27 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
36 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 36 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 36 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 28 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
37 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 37 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 37 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 29 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
38 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 38 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 38 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 30 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
39 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 39 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 39 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 31 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
40 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 40 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 40 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 32 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.5 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
41 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 41 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 41 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 17 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
42 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 42 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 42 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 18 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
43 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 43 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 43 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 19 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
44 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 44 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 44 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 20 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
45 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 45 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 45 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 21 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
46 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 46 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 46 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 22 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
47 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 47 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 47 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 23 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
</TR>
<TR><TD ALIGN="RIGHT"><FONT SIZE="-1">
48 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 48 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 2.0 </FONT></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><FONT SIZE="-1"> 48 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 24 </FONT></TD>
<TD ALIGN="RIGHT"><FONT SIZE="-1"> 1.0 </FONT></TD>
</TR>
</TABLE></DIV>
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