Updated docs.
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Salvatore Filippone
2017-02-12 18:19:15 +00:00
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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 -->
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<TITLE>psb_scatter -- Scatter Global Dense Matrix</TITLE>
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<TITLE>psb_ovrl -- Overlap Update</TITLE>
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@@ -18,123 +18,114 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<H2><A NAME="SECTION00064000000000000000">
psb_scatter -- Scatter Global Dense Matrix</A>
<H2><A NAME="SECTION00062000000000000000">
psb_ovrl -- Overlap Update</A>
</H2>
<P>
These subroutines scatters the portions of global dense matrix owned
by a process to all the processes in the processes grid.
These subroutines applies an overlap operator to the input vector:
<P>
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{displaymath}
loc\_x_i \leftarrow scatter(glob\_x)
x \leftarrow Q x
\end{displaymath}
-->
<IMG
WIDTH="168" HEIGHT="28" BORDER="0"
SRC="img79.png"
ALT="\begin{displaymath}loc\_x_i \leftarrow scatter(glob\_x) \end{displaymath}">
WIDTH="55" HEIGHT="27" BORDER="0"
SRC="img59.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="img70.png"
ALT="$glob\_x$"></STRONG></DT>
<DD>is the global matrix <!-- MATH
$glob\_x_{1:m,1:n}$
-->
<IMG
WIDTH="91" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img71.png"
ALT="$glob\_x_{1:m,1:n}$">
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></STRONG></DT>
<DD>is the global dense submatrix <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">
</DD>
<DT><STRONG><IMG
WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img72.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="53" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img80.png"
ALT="$scatter$"></STRONG></DT>
<DD>is the scatter function.
WIDTH="16" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img60.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="img61.png"
ALT="$ P_a$"> and <IMG
WIDTH="26" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
SRC="img62.png"
ALT="$ P^{T}$">.
</DD>
</DL>
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="3260"></A>
<DIV ALIGN="CENTER"><A NAME="3337"></A>
<TABLE>
<CAPTION><STRONG>Table 17:</STRONG>
<CAPTION><STRONG>Table 15:</STRONG>
Data types</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><IMG
WIDTH="33" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img74.png"
ALT="$x_i, y$"></TD>
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$"></TD>
<TD ALIGN="LEFT"><B>Subroutine</B></TD>
</TR>
<TR><TD ALIGN="LEFT">Integer</TD>
<TD ALIGN="LEFT">psb_scatter</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">psb_scatter</TD>
<TD ALIGN="LEFT">psb_ovrl</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">psb_scatter</TD>
<TD ALIGN="LEFT">psb_ovrl</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Complex</TD>
<TD ALIGN="LEFT">psb_scatter</TD>
<TD ALIGN="LEFT">psb_ovrl</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Complex</TD>
<TD ALIGN="LEFT">psb_scatter</TD>
<TD ALIGN="LEFT">psb_ovrl</TD>
</TR>
</TABLE>
</DIV>
@@ -146,12 +137,13 @@ Data types</CAPTION>
<P>
<BR>
<IMG
WIDTH="539" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="img81.png"
WIDTH="577" HEIGHT="35" ALIGN="BOTTOM" BORDER="0"
SRC="img63.png"
ALT="\begin{lstlisting}
call psb_scatter(glob_x, loc_x, desc_a, info, root, mold)
call psb_ovrl(x, desc_a, info)
call psb_ovrl(x, desc_a, info, update=update_type, work=work)
\end{lstlisting}">
<BR>
<BR>
<P>
<DL>
@@ -161,16 +153,21 @@ call psb_scatter(glob_x, loc_x, desc_a, info, root, mold)
<DT><STRONG><B>On Entry</B></STRONG></DT>
<DD>
</DD>
<DT><STRONG>glob_x</STRONG></DT>
<DD>The array that must be scattered into local pieces.
<DT><STRONG>x</STRONG></DT>
<DD>global dense matrix <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>
Scope: <B>global</B>
Scope: <B>local</B>
<BR>
Type: <B>required</B>
Type: <B>required</B>
<BR>
Intent: <B>in</B>.
Intent: <B>inout</B>.
<BR>
Specified as: a rank one or two array.
Specified as: a rank one or two array or an object of type vdata<TT>psb_T_vect_type</TT>
containing numbers of type specified in
Table&nbsp;<A HREF="#tab:f90ovrl">15</A>.
</DD>
<DT><STRONG>desc_a</STRONG></DT>
<DD>contains data structures for communications.
@@ -183,58 +180,75 @@ Intent: <B>in</B>.
<BR>
Specified as: a structured data of type descdata<TT>psb_desc_type</TT>.
</DD>
<DT><STRONG>root</STRONG></DT>
<DD>The process that holds the global copy. If <IMG
WIDTH="74" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img76.png"
ALT="$root=-1$"> all
the processes have a copy of the global vector.
<DT><STRONG>update</STRONG></DT>
<DD>Update operator.
<BR><DL>
<DT><STRONG>update = psb_none_</STRONG></DT>
<DD>Do nothing;
</DD>
<DT><STRONG>update = psb_add_</STRONG></DT>
<DD>Sum overlap entries, i.e. apply <IMG
WIDTH="26" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
SRC="img64.png"
ALT="$P^T$">;
</DD>
<DT><STRONG>update = psb_avg_</STRONG></DT>
<DD>Average overlap entries, i.e. apply <IMG
WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
SRC="img65.png"
ALT="$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="img66.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>in</B>.
Intent: <B>inout</B>.
<BR>
Specified as: an integer variable <!-- MATH
$-1\le root\le np-1$
-->
<IMG
WIDTH="141" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img77.png"
ALT="$-1\le root\le np-1$">, default
<code>psb_root_</code>, i.e. process 0.
</DD>
<DT><STRONG>mold</STRONG></DT>
<DD>The desired dynamic type for the internal vector storage.
<BR>
Scope: <B>local</B>.
<BR>
Type: <B>optional</B>.
<BR>
Intent: <B>in</B>.
<BR>
Specified as: an object of a class derived from vbasedata<TT>psb_T_base_vect_type</TT>; this is
only allowed when loc_x is of type vdata<TT>psb_T_vect_type</TT>.
Specified as: a one dimensional array of the same type of <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<P>
</DD>
<DT><STRONG><B>On Return</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="img70.png"
ALT="$glob\_x$">.
<DT><STRONG>x</STRONG></DT>
<DD>global dense result matrix <IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img20.png"
ALT="$x$">.
<BR>
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 ALLOCATABLE array or an object of type vdata<TT>psb_T_vect_type</TT> containing numbers of the type
indicated in Table&nbsp;<A HREF="#tab:scatter">17</A>.
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.
@@ -249,29 +263,502 @@ 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="26" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
SRC="img62.png"
ALT="$ P^{T}$"> performs the reduction sum of overlap
elements; it is a ``prolongation'' operator <IMG
WIDTH="26" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
SRC="img64.png"
ALT="$P^T$"> that
replicates overlap elements, accounting for the physical replication
of data;
</LI>
<LI>The operator <IMG
WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img61.png"
ALT="$ 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="3339"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 8:</STRONG>
Sample discretization mesh.</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<IMG
WIDTH="534" HEIGHT="454" ALIGN="BOTTOM" BORDER="0"
SRC="img68.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="img67.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="node66.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="13" HEIGHT="14" 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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