Further Notes

Efficiency

The Interactive Matrix Language is an interpretive language executor that can be characterized as follows:

• efficient and inexpensive to compile
• inefficient and expensive for the number of operations executed
• efficient and inexpensive within each operation

Therefore, you should try to substitute matrix operations for iterative loops. There is a high overhead involved in executing each instruction; however, within the instruction IML runs very efficiently.

Consider the following four methods of summing the elements of a matrix:

  
    s=0;                      /* method 1 */ 
    do i=1 to m; 
       do j=1 to n; 
          s=s+x[i,j]; 
       end; 
    end; 
    s=j[1,m]*x*j[n,1];        /* method 2 */ 
    s=x[+,+];                 /* method 3 */ 
    s=sum(x);                 /* method 4 */
 

Method 1 is the least efficient, method 2 is more efficient, method 3 is more efficient yet, and method 4 is the most efficient. The greatest advantage of using IML is reducing human programming labor.