Outer product capability for dyadic functions in IML

rbettinger — Tue, 01 Aug 2023 18:39:34 GMT

I have written an IML module to compute a table created by the application of a dyadic function ( '+', '#', '/', etc.) applied to two numeric vectors.

start o_p( dyadic_fcn, x, y ) ;
   /* purpose: compute outer product of vectors x, y by applying dyadic function
    *
    * parameters:
    *    dyadic_fcn ::= quoted dyadic function, e.g., + - = ^= # ## < > , &cetera
    *    x          ::= numeric scalar or vector
    *    y          ::= numeric scalar or vector
    *
    * returns outer product of column vector x <dyadic function> row vector y
    *
    *  example:
    *    a = 1 : 4 ; b = 1 : 5 ;
    *
    *    c = op( '/', a, b ) ;
    */

   tmp_x = colvec( x ) ; n_row_x = nrow( tmp_x ) ; 
   tmp_y = rowvec( y ) ; n_col_y = ncol( tmp_y ) ;

   x_mat = repeat( tmp_x, 1, n_col_y ) ;
   y_mat = repeat( tmp_y, n_row_x, 1 ) ;
   
   call execute( 'rslt = x_mat', dyadic_fcn, 'y_mat ;' ) ;
   
   return rslt ;
finish o_p ;

For example,

x = 1 : 5 ;
y = 1 : 3 ;

z1 = o_p( '<', x, y ) ;
z2 = o_p( '+', x, y ) ;
z3 = o_p( '^=', x, y ) ;
z4 = o_p( '#', x, y ) ;

print x y, z1[ l="dyadic function =' '<'"] " " z2[l="dyadic function = '+'"] " " z3[l="dyadic function = '^='"] " " z4[l="dyadic function = '#'"] ;

z = o_p( '#', 1, { 2 3 4 5 } ) ;
print z ;

produces the results

x 	  	y 	 
1 	2 	3 	4 	5 	1 	2 	3
dyadic function =' '<' 	  	dyadic function = '+' 	  	dyadic function = '^=' 	  	dyadic function = '#' 	 
0 	1 	1 	  	2 	3 	4 	  	0 	1 	1 	  	1 	2 	3
0 	0 	1 	  	3 	4 	5 	  	1 	0 	1 	  	2 	4 	6
0 	0 	0 	  	4 	5 	6 	  	1 	1 	0 	  	3 	6 	9
0 	0 	0 	  	5 	6 	7 	  	1 	1 	1 	  	4 	8 	12
0 	0 	0 	  	6 	7 	8 	  	1 	1 	1 	  	5 	10 	15
z
2 	3 	4 	5

I have solved the problem using conformable matrices, but it would be nice if there were an IML function to perform the same task more efficiently. I also know that I can use the APPLY function, but I have to define the particular dyadic function for two arguments, and this is an inelegant and inefficient use of APPLY, IMHO. The statement

  z = colvec( x ) * rowvec( y ) ;

produces the same result as z = o_p( '#', x, y ) but this is the only case of a built-in IML outer product function that I know of. Is there any equivalent in IML for general dyadic functions?

Re: Outer product capability for dyadic functions in IML

Rick_SAS — Tue, 01 Aug 2023 20:13:50 GMT

Interesting. I haven't seen the term 'dyadic function' use like this before. Looks like your 'dyadic functions' are the pairwise scalar operators

D[i,j] = x[i] op y[j]

Although I almost always recommend IML functions over SAS macros, but this might be a case where a macro is simpler:

proc iml;
/* use macro instead of a function call */
%macro o_p(x, op, y);
    (colvec(&x) &op repeat(rowvec(&y),nrow(&x)*ncol(&x)))
%mend;

x = 1 : 5 ;
y = 1 : 3 ;
w1 = %o_p(x, <, y );
w2 = %o_p(x, +, y );
w3 = %o_p(x, ^=, y );
w4 = %o_p(x, #, y );
print w1[r=x c=y l="dyadic function = '<'"],
      w2[r=x c=y l="dyadic function = '+'"], 
      w3[r=x c=y l="dyadic function = '^='"],
      w4[r=x c=y l="dyadic function = '#'"];

topic Outer product capability for dyadic functions in IML in SAS/IML Software and Matrix Computations

Outer product capability for dyadic functions in IML

Re: Outer product capability for dyadic functions in IML