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Added HTML version of manual.
17 years ago
HREF="node1.html">Contents</A></B>
<BR>
<BR></DIV>
psblas2: docs/html docs/html/footnode.html docs/html/img1.png docs/html/img10.png docs/html/img100.png docs/html/img101.png docs/html/img102.png docs/html/img103.png docs/html/img104.png docs/html/img105.png docs/html/img106.png docs/html/img107.png docs/html/img108.png docs/html/img109.png docs/html/img11.png docs/html/img110.png docs/html/img111.png docs/html/img112.png docs/html/img113.png docs/html/img114.png docs/html/img115.png docs/html/img116.png docs/html/img117.png docs/html/img118.png docs/html/img119.png docs/html/img12.png docs/html/img120.png docs/html/img121.png docs/html/img122.png docs/html/img123.png docs/html/img124.png docs/html/img125.png docs/html/img126.png docs/html/img127.png docs/html/img128.png docs/html/img129.png docs/html/img13.png docs/html/img130.png docs/html/img131.png docs/html/img132.png docs/html/img133.png docs/html/img134.png docs/html/img135.png docs/html/img136.png docs/html/img137.png docs/html/img138.png docs/html/img139.png 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Added HTML version of manual.
17 years ago
<!--End of Navigation Panel-->
<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="3546"></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>
psblas3: Changelog docs/html/footnode.html docs/html/img1.png docs/html/img10.png docs/html/img100.png docs/html/img101.png docs/html/img102.png docs/html/img103.png docs/html/img104.png docs/html/img105.png docs/html/img106.png docs/html/img107.png docs/html/img108.png docs/html/img109.png docs/html/img11.png docs/html/img110.png docs/html/img111.png docs/html/img112.png docs/html/img113.png docs/html/img114.png docs/html/img115.png docs/html/img116.png docs/html/img117.png docs/html/img118.png docs/html/img119.png docs/html/img12.png docs/html/img120.png docs/html/img121.png docs/html/img122.png docs/html/img123.png docs/html/img124.png docs/html/img125.png docs/html/img126.png docs/html/img127.png docs/html/img128.png docs/html/img129.png docs/html/img13.png docs/html/img130.png docs/html/img131.png docs/html/img132.png docs/html/img133.png docs/html/img134.png docs/html/img135.png docs/html/img136.png docs/html/img137.png docs/html/img138.png docs/html/img139.png docs/html/img14.png docs/html/img140.png docs/html/img142.png docs/html/img144.png docs/html/img145.png docs/html/img146.png docs/html/img147.png docs/html/img148.png docs/html/img149.png docs/html/img15.png docs/html/img150.png docs/html/img151.png docs/html/img152.png docs/html/img153.png docs/html/img154.png docs/html/img155.png docs/html/img156.png docs/html/img157.png docs/html/img158.png docs/html/img159.png docs/html/img16.png docs/html/img160.png docs/html/img161.png docs/html/img162.png docs/html/img163.png docs/html/img164.png docs/html/img165.png docs/html/img17.png docs/html/img18.png docs/html/img19.png docs/html/img2.png docs/html/img20.png docs/html/img21.png docs/html/img22.png docs/html/img23.png docs/html/img24.png docs/html/img25.png docs/html/img26.png docs/html/img27.png docs/html/img28.png docs/html/img29.png docs/html/img3.png docs/html/img30.png docs/html/img31.png docs/html/img32.png docs/html/img33.png docs/html/img34.png docs/html/img35.png docs/html/img36.png docs/html/img37.png docs/html/img38.png docs/html/img39.png docs/html/img4.png docs/html/img40.png docs/html/img41.png docs/html/img42.png docs/html/img43.png docs/html/img44.png docs/html/img45.png docs/html/img46.png docs/html/img47.png docs/html/img48.png docs/html/img49.png docs/html/img5.png docs/html/img50.png docs/html/img51.png docs/html/img52.png docs/html/img53.png docs/html/img54.png docs/html/img55.png docs/html/img56.png docs/html/img57.png docs/html/img58.png docs/html/img59.png docs/html/img6.png docs/html/img60.png docs/html/img61.png docs/html/img62.png docs/html/img63.png docs/html/img64.png docs/html/img65.png docs/html/img66.png docs/html/img67.png docs/html/img68.png docs/html/img69.png docs/html/img7.png docs/html/img70.png docs/html/img71.png docs/html/img72.png docs/html/img73.png docs/html/img74.png docs/html/img75.png docs/html/img76.png docs/html/img77.png docs/html/img78.png docs/html/img79.png docs/html/img8.png docs/html/img80.png docs/html/img81.png docs/html/img82.png docs/html/img83.png docs/html/img84.png docs/html/img85.png docs/html/img86.png docs/html/img87.png docs/html/img88.png docs/html/img89.png docs/html/img9.png docs/html/img90.png docs/html/img91.png docs/html/img92.png docs/html/img93.png docs/html/img94.png docs/html/img95.png docs/html/img96.png docs/html/img97.png docs/html/img98.png docs/html/img99.png docs/html/index.html docs/html/node1.html docs/html/node10.html docs/html/node100.html docs/html/node101.html docs/html/node102.html docs/html/node103.html docs/html/node104.html docs/html/node105.html docs/html/node106.html docs/html/node107.html docs/html/node108.html docs/html/node109.html docs/html/node11.html docs/html/node110.html docs/html/node111.html docs/html/node112.html docs/html/node113.html docs/html/node114.html docs/html/node115.html docs/html/node116.html docs/html/node117.html docs/html/node118.html docs/html/node119.html docs/html/node12.html docs/html/node120.html docs/html/node121.html docs/html/node122.html docs/html/node123.html docs/html/node124.html docs/html/node125.html docs/html/node126.html docs/html/node127.html docs/html/node128.html docs/html/node13.html docs/html/node14.html docs/html/node15.html docs/html/node16.html docs/html/node17.html docs/html/node18.html docs/html/node19.html docs/html/node2.html docs/html/node20.html docs/html/node21.html docs/html/node22.html docs/html/node23.html docs/html/node24.html docs/html/node25.html docs/html/node26.html docs/html/node27.html docs/html/node28.html docs/html/node29.html docs/html/node3.html docs/html/node30.html docs/html/node31.html docs/html/node32.html docs/html/node33.html docs/html/node34.html docs/html/node35.html docs/html/node36.html docs/html/node37.html docs/html/node38.html docs/html/node39.html docs/html/node4.html docs/html/node40.html docs/html/node41.html docs/html/node42.html docs/html/node43.html docs/html/node44.html docs/html/node45.html docs/html/node46.html docs/html/node47.html docs/html/node48.html docs/html/node49.html docs/html/node5.html docs/html/node50.html docs/html/node51.html docs/html/node52.html docs/html/node53.html docs/html/node54.html docs/html/node55.html docs/html/node56.html docs/html/node57.html docs/html/node58.html docs/html/node59.html docs/html/node6.html docs/html/node60.html docs/html/node61.html docs/html/node62.html docs/html/node63.html docs/html/node64.html docs/html/node65.html docs/html/node66.html docs/html/node67.html docs/html/node68.html docs/html/node69.html docs/html/node7.html docs/html/node70.html docs/html/node71.html docs/html/node72.html docs/html/node73.html docs/html/node74.html docs/html/node75.html docs/html/node76.html docs/html/node77.html docs/html/node78.html docs/html/node79.html docs/html/node8.html docs/html/node80.html docs/html/node81.html docs/html/node82.html docs/html/node83.html docs/html/node84.html docs/html/node85.html docs/html/node86.html docs/html/node87.html docs/html/node88.html docs/html/node89.html docs/html/node9.html docs/html/node90.html docs/html/node91.html docs/html/node92.html docs/html/node93.html docs/html/node94.html docs/html/node95.html docs/html/node96.html docs/html/node97.html docs/html/node98.html docs/html/node99.html docs/html/userhtml.html docs/psblas-3.4.pdf docs/src/datastruct.tex docs/src/userguide.tex docs/src/userhtml.tex docs/src/util.tex test/pargen/runs/ppde.inp Updated docs.
9 years ago
<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="12" HEIGHT="29" 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="3547"></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>
<BR>
<P>
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