A SAS user needed to convert a program from MATLAB into the SAS/IML matrix language and asked whether there is a SAS/IML equivalent to the fliplr and flipud functions in MATLAB. These functions flip the columns or rows (respectively) of a matrix; "LR" stands for "left-right" and "UD" stands for "up-down."

No, SAS/IML does not have equivalent built-in functions, but as Devo once sang: "When a problem comes along, you must whip it." This article shows how to implement these functions in SAS/IML. Or, to paraphrase Devo's maxim: "When a matrix comes along, you must flip it. It's not too late to flip it. Flip it good!"

The FLIPLR and FLIPUD functions in SAS/IML

The key to reversing the columns or rows of a matrix is to use subscript notation. Recall that in the SAS/IML language, the expression A[ ,1] extracts the first column of A. (When the row subscript is not specified, it means "use all rows.") Similarly, A[ ,1:3] extracts the first three columns of A (in order), whereas A[ ,3:1] extracts the first three columns of A in reverse order. A similar notation is valid for rows. The expression A[3:1, ] extracts the first three rows of A in reverse order. Therefore, the following SAS/IML functions implement the functionality of the fliplr and flipud functions for matrices:

proc iml;
/* reverse columns of a matrix */
start fliplr(A);
   return A[ , ncol(A):1];
finish;
 
/* reverse rows of a matrix */
start flipud(A);
   return A[nrow(A):1, ];
finish;
 
/* test the functions on a 2x3 matrix */
x = {1 2 3, 4 5 6};
lr = fliplr(x);
ud = flipud(x);
print x, lr, ud;

Reversing all elements

You can also reverse all elements of a matrix. Recall that a SAS/IML matrix is stored in row-major order, which means that the elements are enumerated by counting across the first row, then across the second row, and so forth. Thus if A is an n x m matrix, then A[n*m:1] returns the elements of A in reverse order. However, the elements are returned in a column vector. If you want the elements in a matrix that has the same dimensions as A, you can "shape it up" by using the SHAPE function, as follows:

/* reverse elements of a matrix */
start reverse(A);
   n = nrow(A); m = ncol(A);
   return shape(A[n*m:1], n, m);     /* Now flip it into SHAPE */
finish;
 
rev = reverse(x);
print rev;

The MATLAB language also supports the rot90 function, which rotates a matrix. I have previously shown how to rotate the elements of a matrix in the SAS/IML language.

In conclusion, although SAS/IML does not contain built-in functions for reversing the rows and columns of a matrix, these functions are easily defined in terms of matrix subscript operations. In short, when given a matrix, it is not hard to flip it, flip it good!