Language Reference

DIAG (matrix) ;

This function is supported by the IML procedure and the iml action.

The DIAG function creates a diagonal matrix. The matrix argument can be either a numeric square matrix or a vector.

If matrix is a square matrix, the DIAG function creates a matrix with diagonal elements equal to the corresponding diagonal elements. All off-diagonal elements in the new matrix are zeros.

If matrix is a vector, the DIAG function creates a matrix with diagonal elements that are the values in the vector. All off-diagonal elements are zeros.

For example, the following statements produce a diagonal matrix by extracting the diagonal elements of a square matrix:

  a = {4 3,
       2 1};
  c = diag(a);
  print c;

The following statements produce a diagonal matrix by using the elements of a vector:

  b = {1 2 3};
  d = diag(b);
  print d;

The DIAG function is useful, but is not always necessary. Most multiplication operations with diagonal matrices can be accomplished by using the elementwise multiplication operator. To add or subtract from the diagonal of a matrix, you can directly reference the matrix elements, as shown in the following example:

A = j(5,5,1);
v = T(1:5);
D = diag(v);

/* overwrite A with A + diag(v) */
/* method 1: less efficient */
A = j(5,5,1);
A = A + diag(v);         /* explicitly form 5x5 diagonal matrix */

/* method 2: more efficient */
A = j(5,5,1);
j = do(1, ncol(A)*nrow(A), ncol(A)+1);      /* {1 7 13 19 25} */
A[j] = vecdiag(A) + v;   /* access diagonal elements directly */