COL Function :: SAS/IML(R) 13.1 User's Guide

COL Function

COL (x) ;

The COL function is part of the IMLMLIB library. The COL function returns a matrix that has the same dimensions as the x matrix and whose $j$ th column has the value $j$ . You can use the COL and ROW function to extract elements of a matrix. For example, the following statements fill the subdiagonal, superdiagonal, and main diagonal of a matrix with a sequence of numbers:

x = j(5, 5, 0);             /* allocate 5 x 5 matrix of zeros */
r = row(x);                 /* create helper matrices */
c = col(x);
idx = loc(abs(r-c)<= 1);    /* indices of sub-, super-, and main diagonal */
x[idx] = 1:ncol(idx);       /* fill with 1,2,3,... */
print x[format=Best3.];

Figure 24.73: A Tridiagonal Matrix

x
1	2	0	0	0
3	4	5	0	0
0	6	7	8	0
0	0	9	10	11
0	0	0	12	13

If r = row(m) and c = col(m) are two matrices, then you can use logical comparisons of r and c to describe certain submatrices, such as in Table 24.1:

Table 24.1: Some Common Submatrices

Submatrix	Index by LOC of
Diagonal	`r = c`
Upper triangular	`r < c`
Lower triangular	`r > c`
Banded with radius $d$	`abs(r-c) <= d`
Antidiagonal	`r + c -1 = ncol(r)`

You can also use the COL function to generate an ID variable when you convert data from a wide format to a long format. For example, the following statements show how to generate a column vector with values $\{ 1, 2, 3, 1, 2, 3, \ldots , 1, 2, 3\}$ :

NumSubjects = 5;        /* number of subjects */
NumRepeated = 3;        /* number of repeated obs per subject */
Y = col(j(NumSubjects, NumRepeated));
Repl = shape(Y, 0, 1);  /* {1, 2, 3, 1, 2, 3, ..., 1, 2, 3}   */