The GRADE and RANK functions each take a matrix M
and return a matrix r with the same dimensions. Each element in
r ranges between 1 and the number of elements n in
M, inclusive. When the elements in M all have unique
values, both of these functions yield the same results: the smallest
element in M corresponds to value 1 in r, the next
smallest to 2, and so on, up to the largest to n. When multiple
elements in M have the same value, these functions use different
rules for handling the ties.
Returns a ranking of M, turning duplicate values into sequential ranks. The returned matrix always contains each of the integers 1 through the number of elements in the matrix exactly once.
GRADE({1, 0, 3; 3, 1, 2; 3, 0, 5}) ⇒ {3, 1, 6; 7, 4, 5; 8, 2, 9}
Returns a ranking of M, turning duplicate values into the mean of their sequential ranks.
RNKORDER({1, 0, 3; 3, 1, 2; 3, 0, 5})
⇒ {3.5, 1.5, 7; 7, 3.5, 5; 7, 1.5, 9}
One may use GRADE to sort a vector:
COMPUTE v(GRADE(v))=v. /* Sort v in ascending order. COMPUTE v(GRADE(-v))=v. /* Sort v in descending order.