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<H2><A NAME="SECTION000422000000000000000">SLA_COMBN - Next Combination</A>
<A NAME="xref_SLA_COMBN"> </A><A NAME="SLA_COMBN"> </A>
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<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Generate the next combination, a subset of a specified size chosen
from a specified number of items.
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_COMBN (NSEL, NCAND, LIST, J)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>NSEL</EM></TD>
<TH ALIGN="LEFT"><B>I</B></TH>
<TD ALIGN="LEFT" NOWRAP>number of items (subset size)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>NCAND</EM></TD>
<TD ALIGN="LEFT"><B>I</B></TD>
<TD ALIGN="LEFT" NOWRAP>number of candidates (set size)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>GIVEN and RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>LIST</EM></TD>
<TH ALIGN="LEFT"><B>I(NSEL)</B></TH>
<TD ALIGN="LEFT" NOWRAP>latest combination, LIST(1)=0 to initialize</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>J</EM></TD>
<TH ALIGN="LEFT"><B>I</B></TH>
<TD ALIGN="LEFT" NOWRAP>status:</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> -1 = illegal NSEL or NCAND</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> 0 = OK</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> +1 = no more combinations available</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>NSEL and NCAND must both be at least 1, and NSEL must be less
than or equal to NCAND.
<DT>2.
<DD>This routine returns, in the LIST array, a subset of NSEL integers
chosen from the range 1 to NCAND inclusive, in ascending order.
Before calling the routine for the first time, the caller must set
the first element of the LIST array to zero (any value less than 1
will do) to cause initialization.
<DT>3.
<DD>The first combination to be generated is:
<BLOCKQUOTE>LIST(1)=1, LIST(2)=2, ..., LIST(NSEL)=NSEL
</BLOCKQUOTE>
This is also the combination returned for the ``finished'' (J=1) case.
The final permutation to be generated is:
<BLOCKQUOTE>LIST(1)=NCAND, LIST(2)=NCAND-1, ..., <BR>
LIST(NSEL)=NCAND-NSEL+1
</BLOCKQUOTE>
<DT>4.
<DD>If the ``finished'' (J=1) status is ignored, the routine
continues to deliver combinations, the pattern repeating
every NCAND!/(NSEL!(NCAND-NSEL)!) calls.
<DT>5.
<DD>The algorithm is by R.F.Warren-Smith (private communication).
</DL></DL>
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<ADDRESS>
<I>SLALIB --- Positional Astronomy Library<BR>Starlink User Note 67<BR>P. T. Wallace<BR>12 October 1999<BR>E-mail:ptw@star.rl.ac.uk</I>
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