Functions and CALL Routines

CALL LEXCOMBI Routine

Generates all combinations of the indices of n objects taken k at a time in lexicographic order.

Category:

Combinatorial

Syntax
Arguments
Details
	CALL LEXCOMBI Processing
	Using the CALL LEXCOMBI Routine with Macros
Comparisons
Examples
	Example 1: Using the CALL LEXCOMBI Routine with the DATA Step
	Example 2: Using the CALL LEXCOMBI Routine with Macros and Displaying the Return Code
See Also

Syntax

CALL LEXCOMBI(n, k, index-1, ..., index-k);

CALL LEXCOMBI Processing

Before the first call to the LEXCOMBI routine, complete one of the following tasks:

Set index-1 equal to zero or to a missing value.
Initialize index-1 through index-k to distinct integers between 1 and n inclusive.

The number of combinations of n objects taken k at a time can be computed as COMB(n,k). To generate all combinations of n objects taken k at a time, call LEXCOMBI in a loop that executes COMB(n,k) times.

Using the CALL LEXCOMBI Routine with Macros

If you call the LEXCOMBI routine from the macro processor with %SYSCALL, then you must initialize all arguments to numeric values. %SYSCALL reformats the values that are returned.

If an error occurs during the execution of the CALL LEXCOMBI routine, then both of the following values are set:

&SYSERR is assigned a value that is greater than 4.
&SYSINFO is assigned a value that is less than -100.

If there are no errors, then &SYSERR is set to zero, and &SYSINFO is set to one of the following values:

1 if the value of variable-1 changed
j if variable-1 through variable-i did not change, but variable-j did change, where j=i+1
-1 if all distinct combinations have already been generated

Comparisons

The CALL LEXCOMBI routine generates all combinations of the indices of n objects taken k at a time in lexicographic order. The CALL ALLCOMBI routine generates all combinations of the indices of n objects taken k at a time in a minimum change order.

Examples

Example 1: Using the CALL LEXCOMBI Routine with the DATA Step

The following example uses the CALL LEXCOMBI routine to generate combinations of indices in lexicographic order.

data _null_;
   array x[5] $3 ('ant' 'bee' 'cat' 'dog' 'ewe');
   array c[3] $3;
   array i[3];
   n=dim(x);
   k=dim(i);
   i[1]=0;
   ncomb=comb(n,k);
   do j=1 to ncomb;
      call lexcombi(n, k, of i[*]);
      do h=1 to k;
         c[h]=x[i[h]];
      end;
      put @4 j= @10 'i= ' i[*] +3 'c= ' c[*];
   end;
run;

SAS writes the following output to the log:

   j=1   i= 1 2 3    c= ant bee cat
   j=2   i= 1 2 4    c= ant bee dog
   j=3   i= 1 2 5    c= ant bee ewe
   j=4   i= 1 3 4    c= ant cat dog
   j=5   i= 1 3 5    c= ant cat ewe
   j=6   i= 1 4 5    c= ant dog ewe
   j=7   i= 2 3 4    c= bee cat dog
   j=8   i= 2 3 5    c= bee cat ewe
   j=9   i= 2 4 5    c= bee dog ewe
   j=10  i= 3 4 5    c= cat dog ewe

Example 2: Using the CALL LEXCOMBI Routine with Macros and Displaying the Return Code

The following example uses the CALL LEXCOMBI routine with macros. The output includes values for the %SYSINFO macro.

%macro test;
   %let x1=0;
   %let x2=0;
   %let x3=0;
   %let n=5;
   %let k=3;
   %let ncomb=%sysfunc(comb(&n,&k));
   %do j=1 %to &ncomb+1;
      %syscall lexcombi(n,k,x1,x2,x3);
      %let jfmt=%qsysfunc(putn(&j,5.));
      %let pad=%qsysfunc(repeat(%str(),6-%length(&x1 &x2 &x3)));
      %put &jfmt: &x1 &x2 &x3 &pad sysinfo=&sysinfo;
   %end;
%mend;

%test