LOGICALOPS Logical Array Operators
Section: Mathematical Operators
Usage
There are three Boolean operators available in FreeMat. The syntax for their use is:y = ~x y = a & b y = a | b
where x
, a
and b
are logical
arrays. The operators are
- NOT (
~
) - outputy
is true if the corresponding element ofx
is false, and ouputy
is false if the corresponding element ofx
is true. - OR (
|) - output
y
is true if corresponding element ofa
is true or if corresponding element ofb
is true (or if both are true). - AND (
\&
) - outputy
is true only if both the corresponding elements ofa
andb
are both true.
shortcut
evaluation. This means that
if we have two expressions
if (expr1 & expr2)
then if expr1
evaluates to false
, then expr2
is not evaluated at all.
Similarly, for the expression
if (expr1 | expr2)
then if expr1
evaluates to true
, then expr2
is not evaluated at all.
Shortcut evaluation is useful for doing a sequence of tests, each of which is
not valid unless the prior test is successful. For example,
if isa(p,'string') & strcmp(p,'fro')
is not valid without shortcut evaluation (if p
is an integer, for example,
the first test returns false, and an attempt to evaluate the second expression
would lead to an error). Note that shortcut evaluation only works with scalar
expressions.
Examples
Some simple examples of logical operators. Suppose we want to calculate the exclusive-or (XOR) of two vectors of logical variables. First, we create a pair of vectors to perform the XOR operation on:--> a = (randn(1,6)>0) a = 0 1 1 1 0 1 --> b = (randn(1,6)>0) b = 0 1 0 0 1 0
Next, we can compute the OR of a
and b
:
--> c = a | b c = 0 1 1 1 1 1
However, the XOR and OR operations differ on the fifth entry - the XOR would be false, since it is true if and only if exactly one of the two inputs is true. To isolate this case, we can AND the two vectors, to find exactly those entries that appear as true in both a
and b
:
--> d = a & b d = 0 1 0 0 0 0
At this point, we can modify the contents of c
in two ways -- the Boolean way is to AND \sim d
with c
, like so
--> xor = c & (~d) xor = 0 0 1 1 1 1
The other way to do this is simply force c(d) = 0
, which uses the logical indexing mode of FreeMat (see the chapter on indexing for more details). This, however, will cause c
to become an int32
type, as opposed to a logical type.
--> c(d) = 0 c = 0 0 1 1 1 1