Element-by-element Boolean Operators

An element-by-element boolean expression is a combination of comparison expressions using the boolean operators "or" (|) "and" (&), and "not" (!), along with parentheses to control nesting. The truth of the boolean expression is computed by combining the truth values of the corresponding elements of the component expressions. A value is considered to be false if it is zero and true otherwise.

Element-by-element boolean expressions can be used wherever comparison expressions can be used. They can be used in if and while statements. However if a matrix value used as the condition in an if or while statement is only true if all of its elements are nonzero.

Like comparison operations each element of an element-by-element boolean expression also has a numeric value (1 if true 0 if false) that comes into play if the result of the boolean expression is stored in a variable or used in arithmetic.

Here are descriptions of the three element-by-element boolean operators.

boolean1 & boolean2

Elements of the result are true if both corresponding elements of boolean1 and boolean2 are true.

boolean1 | boolean2

Elements of the result are true if either of the corresponding elements of boolean1 or boolean2 is true.

! boolean

~ boolean

Each element of the result is true if the corresponding element of boolean is false.

For matrix operands these operators work on an element-by-element basis. For example the expression

     [1 0; 0, 1] & [1, 0; 2, 3]
     

returns a two by two identity matrix.

For the binary operators the dimensions of the operands must conform if both are matrices. If one of the operands is a scalar and the other a matrix the operator is applied to the scalar and each element of the matrix.

For the binary element-by-element boolean operators both subexpressions boolean1 and boolean2 are evaluated before computing the result. This can make a difference when the expressions have side effects. For example in the expression

     a & b++
     

the value of the variable b is incremented even if the variable a is zero.

This behavior is necessary for the boolean operators to work as described for matrix-valued operands.