ELEMENT Function

ELEMENT (x, y) ;

The ELEMENT function returns a matrix that is the same shape as x. The return value indicates which elements of x are elements of y. In particular, if A = element(x, y), then

\[  A_ i = \left\{  \begin{array}{ll} 1 &  \mbox{if}~  x_ i \in y \\ 0 &  \mbox{otherwise} \end{array} \right.  \]

The arguments are as follows:

x

specifies a matrix of elements to test for membership.

y

specifies a set.

If the intersection between x and y is empty, then the ELEMENT function returns a zero matrix. If x is a proper subset of y, then the ELEMENT function returns a matrix of ones. In general, the ELEMENT function returns 1 for elements in the intersection of x and y, as shown in the following statements:

x = {0, 0.5, 1, 1.5, 2, 2.5, 3, 0.5, 1.5, 3, 3, 1};
set = {0 1 3}`;
b = element(x, set);

n = sum(b);        /* number of elements of X that are in SET */
idx = t(loc(b));   /* indices of elements of X that are in SET */
values = x[idx];   /* values of elements of X that are in SET */
print n idx values;

Figure 24.121: Elements That Belong to a Set

n idx values
6 1 0
  3 1
  7 3
  10 3
  11 3
  12 1