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Compound Expressions

With SAS/IML software, you can write compound expressions involving several matrix operators and operands. For example, the following statements are valid matrix assignment statements:

  
    a=x+y+z; 
    a=x+y*z\prime ; 
    a=(-x)#(y-z);
 

The rules for evaluating compound expressions are as follows:

• Evaluation follows the order of operator precedence, as described in Table 4.1. Group I has the highest priority; that is, group I operators are evaluated first. Group II operators are evaluated after group I operators, and so forth. Consider the following statement:

    
            a=x+y*z;
   

  This statement first multiplies matrices and since the * operator (group II) has higher precedence than the + operator (group III). It then adds the result of this multiplication to the matrix and assigns the new matrix to .
• If neighboring operators in an expression have equal precedence, the expression is evaluated from left to right, except for the group I operators. Consider the following statement:

    
            a=x/y/z;
   

  This statement first divides each element of matrix by the corresponding element of matrix . Then, using the result of this division, it divides each element of the resulting matrix by the corresponding element of matrix . The operators in group I, described in Table 4.1, are evaluated from right to left. For example, the following expression is evaluated as :

    
            -x**2
   

When multiple prefix or postfix operators are juxtaposed, precedence is determined by their order from inside to outside.

For example, the following expression is evaluated as :

  
          a`[i,j]
 

All expressions enclosed in parentheses are evaluated first, using the two preceding rules. Consider the following statement:

  
          a=x/(y/z);
 

This statement is evaluated by first dividing elements of by the elements of , then dividing this result into .