Just for fun I wrote the IML module below to return an n x n Pascal matrix.  The lower triangular part of the matrix contains Pascal's triangle, and it is zero above the main diagonal. start Pascal( n );   a = row( j(n, n) ) >= col( j(n, n) );   return( a # comb( (row(a) - 1) # a, (col(a) - 1) # a ) ); finish; It occurred to me that the COMB function makes this much harder than it should be, as ideally I would like COMB(n,r) to return zero when r>n, rather than returning a missing value. Compare this to Wolfram Alpha which does return zero, as it evaluates factorials of negative integers to be infinite (Google does the same when you enter something like '1 choose 2'). If you would like to try the module, the Pascal matrix certainly has an interesting inverse and its back-diagnonals sum to the Fibonacci numbers. ... View more

In general when I press the Break button to interrupt a CPU intensive IML program, I find that it is extremely unresponsive.  If I am patient it will run for many minutes before it releases control back to me, so instead I resort to killing SAS in the Windows Task Manager, but only provided I have remembered to save what I was doing! I have fudged a way around this.  In my main program loop, I am considering using syntax like:     do i = 1 to 1E10;       if mod(i, 1E5) = 0 then do;         call push("resume;");         pause;       end;       < do stuff here >     end; In my tests, this does make IML much more responsive to pressing the break button. But you either have to put up with the flood of notes to the log window, or kill notes for the whole program.  Is there a better way?  A system option perhaps? A different way of structuring my IML program?  I am using 9.4 in Windows 7. ... View more

An IML program that provides simple functions for making four varieties of Latin square that are useful in combinatorics and experimental design.  One of these functions generates Williams Latin squares that are frequently used whenever a sequence of different treatments or samples are evaluated by the same subject.   Three further utility functions for the statistical randomization of Latin squares are also provided.   Finally a Latin square based construction of a tournament design is developed which has applications to the scheduling of leagues.   ... View more

The macro generates Sudoku puzzles using a two-stage algorithm.   Initially it finds a completed Sudoku square using a Markov chain algorithm that tries to sample at random from all squares that exist. The macro is not restricted to 9x9 squares and can generate squares up to 25x25 within a reasonable amount of time.  In the field of experimental design, these squares are known as gerechte designs with rectangular regions.  The second stage algorithm uses very simple reverse solving logic to generate a valid puzzle, by removing clues one by one from the completed square.  The puzzle generated is written to a SAS data set in the work library and can also be viewed as listing output or as RTF/PDF files. ... View more