The ALL function returns a value of 1 if all elements in matrix are nonzero. If any element of matrix is zero or missing, the ALL function returns a value of 0.

You can use the ALL function to express the results of a comparison operator as a single 1 or 0. For example, the following statement compares elements in two matrices:

a = { 1 2, 3 4};
b = {-1 0, 0 1};
if all(a>b) then
   msg = "a[i,j] > b[i,j] for all i,j";
else
   msg = "for some element, a[i,j] is not greater than b[i,j]";
print msg;

In the preceding statements, the comparison operation a>b creates a matrix of zeros and ones. The ALL function returns a value of 1 because every element of a is greater than the corresponding element of b.

The ALL function is implicitly applied to the evaluation of all conditional expressions, so in fact the previous IF-THEN statement is equivalent to the following:

if a>b then       /* implicit ALL */
   msg = "a[i,j] > b[i,j] for all i,j";