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<H2><A NAME="SECTION00062000000000000000">
psb_ovrl -- Overlap Update</A>
</H2>

<P>
These subroutines applies an overlap operator to the input vector:

<P>
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH
 \begin{displaymath}
x \leftarrow Q x
\end{displaymath}
 -->

<IMG
 WIDTH="55" HEIGHT="27" BORDER="0"
 SRC="img60.png"
 ALT="\begin{displaymath}x \leftarrow Q x \end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
where:
<DL>
<DT><STRONG><IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$"></STRONG></DT>
<DD>is the global dense submatrix <IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$">
</DD>
<DT><STRONG><IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img61.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="img62.png"
 ALT="$ P_a$"> and <IMG
 WIDTH="27" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="img63.png"
 ALT="$ P^{T}$">. 
</DD>
</DL>

<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="3208"></A>
<TABLE>
<CAPTION><STRONG>Table 15:</STRONG>
Data types</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$"></TD>
<TD ALIGN="LEFT"><B>Subroutine</B></TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">psb_ovrl</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">psb_ovrl</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Complex</TD>
<TD ALIGN="LEFT">psb_ovrl</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Complex</TD>
<TD ALIGN="LEFT">psb_ovrl</TD>
</TR>
</TABLE>
</DIV>
</TD></TR>
</TABLE>
</DIV><P></P>
<BR>

<P>
<BR>
<IMG
 WIDTH="576" HEIGHT="35" ALIGN="BOTTOM" BORDER="0"
 SRC="img64.png"
 ALT="\begin{lstlisting}
call psb_ovrl(x, desc_a, info)
call psb_ovrl(x, desc_a, info, update=update_type, work=work)
\end{lstlisting}">
<BR> 

<P>
<DL>
<DT><STRONG>Type:</STRONG></DT>
<DD>Synchronous.
</DD>
<DT><STRONG><B>On Entry</B></STRONG></DT>
<DD>
</DD>
<DT><STRONG>x</STRONG></DT>
<DD>global dense matrix <IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$">.
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>required</B> 
<BR>
Intent: <B>inout</B>.
<BR>
Specified as:  a rank one or two array or an object of type vdata<TT>psb_T_vect_type</TT> 
containing numbers of type specified in
Table&nbsp;<A HREF="#tab:f90ovrl">15</A>.
</DD>
<DT><STRONG>desc_a</STRONG></DT>
<DD>contains data structures for communications.
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>required</B>
<BR>
Intent: <B>in</B>.
<BR>
Specified as: a structured data of type descdata<TT>psb_desc_type</TT>.
</DD>
<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="27" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="img65.png"
 ALT="$P^T$">;
</DD>
<DT><STRONG>update = psb_avg_</STRONG></DT>
<DD>Average overlap entries, i.e. apply <IMG
 WIDTH="44" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="img66.png"
 ALT="$P_aP^T$">;
</DD>
</DL>
Scope: <B>global</B> 
<BR>
Intent: <B>in</B>.
<BR>
Default: <!-- MATH
 $update\_type = psb\_avg\_$
 -->
<IMG
 WIDTH="166" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img67.png"
 ALT="$update\_type = psb\_avg\_ $">
<BR>
Scope: <B>global</B> 
<BR>
Specified as: a integer variable.
</DD>
<DT><STRONG>work</STRONG></DT>
<DD>the work array. 
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>optional</B>
<BR>
Intent: <B>inout</B>.
<BR>
Specified as: a one dimensional array of the same type of <IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$">.

<P>
</DD>
<DT><STRONG><B>On Return</B></STRONG></DT>
<DD>
</DD>
<DT><STRONG>x</STRONG></DT>
<DD>global dense result matrix <IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$">.
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>required</B> 
<BR>
Intent: <B>inout</B>.
<BR>
Specified as: an  array of rank one or two
containing numbers of type specified in
Table&nbsp;<A HREF="#tab:f90ovrl">15</A>.
</DD>
<DT><STRONG>info</STRONG></DT>
<DD>Error code.
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>required</B> 
<BR>
Intent: <B>out</B>.
<BR>
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="img63.png"
 ALT="$ P^{T}$"> performs the reduction sum of overlap
elements; it is a ``prolongation'' operator <IMG
 WIDTH="27" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="img65.png"
 ALT="$P^T$"> that
replicates overlap elements, accounting for the physical replication
of data;
</LI>
<LI>The operator <IMG
 WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img62.png"
 ALT="$ 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="3210"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 8:</STRONG>
Sample discretization mesh.</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<IMG
 WIDTH="533" HEIGHT="453" ALIGN="BOTTOM" BORDER="0"
 SRC="img69.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="img68.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">8</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="node62.html#fig:try8x8">7</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="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.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>
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