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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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<H2><A NAME="SECTION00061000000000000000">
psb_halo -- Halo Data Communication</A>
</H2>
<P>
These subroutines gathers the values of the halo
elements:
<P>
<BR><P></P>
<DIV ALIGN="CENTER" CLASS="mathdisplay">
<!-- MATH
\begin{displaymath}
x \leftarrow x
\end{displaymath}
-->
<IMG
WIDTH="43" HEIGHT="24" BORDER="0"
SRC="img59.png"
ALT="\begin{displaymath}x \leftarrow x \end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
where:
<DL>
<DT><STRONG><SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN></STRONG></DT>
<DD>is a global dense submatrix.
</DD>
</DL>
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="3453"></A>
<TABLE>
<CAPTION><STRONG>Table 14:</STRONG>
Data types</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><SPAN CLASS="MATH"><IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img22.png"
ALT="$\alpha$"></SPAN>, <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN></TD>
<TD ALIGN="LEFT"><B>Subroutine</B></TD>
</TR>
<TR><TD ALIGN="LEFT">Integer</TD>
<TD ALIGN="LEFT">psb_halo</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">psb_halo</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">psb_halo</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Complex</TD>
<TD ALIGN="LEFT">psb_halo</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Complex</TD>
<TD ALIGN="LEFT">psb_halo</TD>
</TR>
</TABLE>
</DIV>
</TD></TR>
</TABLE>
</DIV><P></P>
<BR>
<P>
<BR>
<IMG
WIDTH="395" HEIGHT="35" ALIGN="BOTTOM" BORDER="0"
SRC="img60.png"
ALT="\begin{lstlisting}
call psb_halo(x, desc_a, info)
call psb_halo(x, desc_a, info, work, data)
\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 <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN>.
<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:f90halo">14</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>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 rank one array of the same type of <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN>.
</DD>
<DT><STRONG>data</STRONG></DT>
<DD>index list selector.
<BR>
Scope: <B>global</B>
<BR>
Type: <B>optional</B>
<BR>
Specified as: an integer. Values:<code>psb_comm_halo_</code>,<code>psb_comm_mov_</code>,
<code>psb_comm_ext_</code>, default: <code>psb_comm_halo_</code>. Chooses the
index list on which to base the data exchange.
<P>
</DD>
<DT><STRONG><B>On Return</B></STRONG></DT>
<DD>
</DD>
<DT><STRONG>x</STRONG></DT>
<DD>global dense result matrix <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN>.
<BR>
Scope: <B>local</B>
<BR>
Type: <B>required</B>
<BR>
Intent: <B>inout</B>.
<BR>
Returned as: a rank one or two array
containing numbers of type specified in
Table&nbsp;<A HREF="#tab:f90halo">14</A>.
</DD>
<DT><STRONG>info</STRONG></DT>
<DD>the local portion of result submatrix <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img21.png"
ALT="$y$"></SPAN>.
<BR>
Scope: <B>local</B>
<BR>
Type: <B>required</B>
<BR>
Intent: <B>out</B>.
<BR>
An integer value that contains an error code.
</DD>
</DL>
<DIV ALIGN="CENTER"><A NAME="fig:try8x8"></A><A NAME="3454"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 7:</STRONG>
Sample discretization mesh.</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<IMG
WIDTH="358" HEIGHT="313" ALIGN="BOTTOM" BORDER="0"
SRC="img61.png"
ALT="\includegraphics[scale=0.45]{figures/try8x8.eps}">
<IMG
WIDTH="358" HEIGHT="313" ALIGN="BOTTOM" BORDER="0"
SRC="img62.png"
ALT="\includegraphics[scale=0.45]{figures/try8x8}">
</DIV></TD></TR>
</TABLE>
</DIV>
<P>
<BIG CLASS="LARGE"><B>Usage Example</B></BIG>
Consider the discretization mesh depicted in fig.&nbsp;<A HREF="#fig:try8x8">7</A>,
partitioned among two processes as shown by the dashed line; the data
distribution is such that each process will own 32 entries in the
index space, with a halo made of 8 entries placed at local indices 33
through 40. If process 0 assigns an initial value of 1 to its entries
in the <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></SPAN> vector, and process 1 assigns a value of 2, then after a
call to <code>psb_halo</code> the contents of the local vectors will be the
following:
<BR>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 ALIGN="CENTER">
<TR><TD ALIGN="CENTER" COLSPAN=3><SMALL CLASS="SMALL">
<SPAN>Process 0</SPAN></SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="CENTER" COLSPAN=3><SMALL CLASS="SMALL">
<SPAN>Process 1</SPAN></SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
I </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> GLOB(I) </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> X(I) </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> I </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> GLOB(I) </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> X(I) </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
1 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 33 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
2 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 34 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
3 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 3 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 3 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 35 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
4 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 4 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 4 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 36 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
5 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 5 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 5 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 37 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
6 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 6 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 6 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 38 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
7 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 7 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 7 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 39 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
8 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 8 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 8 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 40 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
9 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 9 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 9 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 41 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
10 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 10 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 10 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 42 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
11 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 11 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 11 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 43 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
12 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 12 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 12 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 44 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
13 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 13 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 13 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 45 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
14 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 14 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 14 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 46 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
15 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 15 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 15 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 47 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
16 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 16 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 16 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 48 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
17 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 17 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 17 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 49 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
18 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 18 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 18 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 50 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
19 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 19 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 19 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 51 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
20 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 20 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 20 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 52 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
21 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 21 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 21 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 53 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
22 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 22 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 22 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 54 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
23 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 23 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 23 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 55 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
24 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 24 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 24 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 56 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
25 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 25 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 25 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 57 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
26 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 26 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 26 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 58 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
27 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 27 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 27 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 59 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
28 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 28 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 28 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 60 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
29 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 29 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 29 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 61 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
30 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 30 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 30 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 62 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
31 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 31 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 31 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 63 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
32 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 32 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 32 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 64 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
33 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 33 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 33 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 25 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
34 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 34 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 34 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 26 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
35 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 35 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 35 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 27 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
36 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 36 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 36 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 28 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
37 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 37 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 37 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 29 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
38 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 38 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 38 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 30 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
39 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 39 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 39 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 31 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">
40 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 40 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 2.0 </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 40 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 32 </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 1.0 </SMALL></TD>
</TR>
</TABLE></DIV>
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