Working with Matrices

More about Missing Values

Missing values in matrices are discussed in Chapter 3: Understanding the SAS/IML Language. You should carefully read that chapter and Chapter 24: Further Notes, so that you are aware of the way SAS/IML software handles missing values. The following examples show how missing values are handled for elementwise operations and for subscript reduction operators.

Consider the following two matrices $\mb{X}$ and $\mb{Y}$:

\[ \mb{X} = \left[ \begin{array}{ccc} 1 & 2 & . \\ . & 5 & 6 \\ 7 & . & 9 \\ \end{array} \right] \mb{Y} = \left[ \begin{array}{ccc} 4 & . & 2 \\ 2 & 1 & 3 \\ 6 & . & 5 \\ \end{array} \right] \]

The following operations handle missing values in matrices:

\[ \mbox{Matrix addition: } \mb{X} +\mb{Y} \mbox{ is } \left[ \begin{array}{ccc} 5 & . & . \\ . & 6 & 9 \\ 13 & . & 14 \\ \end{array} \right] \]
\[ \mbox{Elementwise multiplication: } \mb{X} \# \mb{Y} \mbox{ is } \left[ \begin{array}{ccc} 4 & . & . \\ . & 5 & 18 \\ 42 & . & 45 \\ \end{array} \right] \]
\[ \mbox{Subscript reduction: } \mb{X} [+,] \mbox{ is } \left[ \begin{array}{ccc} 8 & 7 & 15 \\ \end{array} \right] \]