5.1 The Logical Operators: not, and, or, exclusive or
5.2 Associated Logical Functions: any, all, find
5.3 Looking for Special Numbers: NaN and Inf
MATLAB supplies the usual logical operations that find use
particularly in writing MATLAB programs. These consist of logical
operators used for comparisons as shown next:
Example Symbol Meaning
>> a = [1 2 3] ; Equality of numerics -- >> disp(2 == a) Thus, only the second 0 1 0 == element of vector a is equal to 2.
>> disp('b'=='abB') 0 1 0 == Equality of character data
>> disp(2 <= a) 0 1 1 <= Less than or equal for numerics
>> disp('b'<='abcB') 0 1 1 0 <= Less than equal for character data
The examples shown in the table are typical, but the other
comparisons shown next:
|
Symbol |
Meaning |
|
< |
Less than |
|
> |
Greater than |
|
>= |
Greater than or equal |
|
~= |
Not equal |
>> disp(3<5)
1
>> disp(5<3)
0
>> disp(3<3)
0
>> disp(3>=3)
1
>> disp(3==3.1)
0
>> disp(3~=3.1)
1
All of those are easy to understand.
The logical operators all perform directly as we would expect on
vectors as long as they are the same length.
>> disp([1 2]<[-2 2])
0 0
>> disp([1 2]<=[-2 2])
0 1
>> disp([1 2]>[-2 2])
1 0
>> disp([1 2]>=[-2 2])
1 1
>> disp([1 2]==[-2 2])
0 1
>> disp([1 2]~=[-2 2])
1 0
The logical operators all do quite nicely in comparing a scalar to the elements of a vector, but you need to tell whether the comparison or the vector generator is to be done first:
>> disp(2>0:4)
??? disp(2>0:4)
Improper function reference. A "," or ")" is expected.
>> disp(2>(0:4))
1 1 0 0 0
Additional parentheses are needed to made this clear.
Operations on each element of matrices is shown next:
>> m=[1 2 3
2 3 4];
>> disp(m<2)
1 0 0
0 0 0
>> m1=[-1 0 2
0 2 4];
>> disp(m>m1)
1 1 1
1 1 0
5.1 The Logical Operators: not, and, or,
exclusive or
We may also want to string the logical results with 'not,' 'or,'
'and,' and `exclusive or' operations. The ways that `not,' 'or,'
'and,' and `exclusive or' operations perform are shown in the next
Matlab session:
More Logical Operations
>> disp([0 0 1 1] & [0 1 0 1]) <-- & = Logical `and'
0 0 0 1
>> disp([0 0 1 1] | [0 1 0 1]) <-- | = Logical `or'
0 1 1 1
>> disp(~[0 1]) <-- ~ = Logical `not'
1 0
>> disp(xor([0 0 1 1],[0 1 0 1])) <-- xor = Logical `exclusive or'
0 1 1 0
The `not' operator (~) helps transform answers that we get for logical comparisons to ones that we need. It can be applied to any array:
>> disp(m)
1 2 3
2 3 4
>> disp(~0)
1
>> disp(~[0 1])
1 0
>> disp(~m>2)
0 0 0
0 0 0
>> disp(~(m>2))
1 1 0
1 0 0
The examples shown with the matrix m, illustrate two
characteristics of MATLAB. In MATLAB logical operations, any non-zero
number is treated as being 'true'. Secondly, the not operation
is done before the comparison if there are no parentheses as in the
first case with m. Thus from ~m, we got all zeros or ones and then
none of those were found to be greater than 2.
The and operation on logical elements is done with the symbol:
"&" . The or operation on logical elements is done with
the symbol: "|" . These operations work with pairs of logical
elements to produce results as seen in the vector operations used in
our table:
>> disp([0 0 1 1]&[0 1 0 1])
0 0 0 1
>> disp([0 0 1 1]|[0 1 0 1])
0 1 1 1
These extend to pairs of matrices of the same shape and to a matrix combined with a scalar with no problems:
>> m=[0 0
1 1];
>> m1=[0 1
0 1];
>> disp(m&m1)
0 0
0 1
>> disp(m|m1)
0 1
1 1
>> disp(m&1)
0 0
1 1
The exclusive or operation on logical elements is done with the function: xor. This operation accepts a pair of logical elements to produce results as seen in the vector operations used in our table:
>> disp(xor([0 0 1 1],[0 1 0 1]))
0 1 1 0
Be careful to note xor is a function, and the two vectors
of logical elements must be entered in standard function format.
5.2 Associated Logical Functions: any, all,
find
These three functions find frequent use in making programming
decisions about what needs to be done in solving problems. The
function any tells us whether there are any non-zero elements
in a vector as in:
>> v=[-2 1 3 5];
>> disp(any(v<1))
1
>> disp(any(v>6))
0
Since the logical comparison returns 0 for each false comparison and 1 for each true comparison, the function any allows us to find if any of the comparisons are true. The all function tells us if every comparison is true:
>> disp(all(v<1))
0
>> disp(all(v<6))
1
Both of these functions can be applied to matrices. They simply tell us the condition found for each column of the matrix.
>> disp(m)
1 2 3
2 3 4
>> disp(any(m<2))
1 0 0
The find function allows us to locate non-zero elements in an array. It gives the indices of all non-zero elements as seen next:
>> disp(v)
-2 1 3 5
>> disp(find(v>3))
4
>> disp(find(v>0))
2 3 4
You cannot use find with matrices:
>> disp(m)
1 2 3
2 3 4
>> disp(find(m>2))
??? Error using ==> find
Argument must be a vector.
5.3 Looking for Special Numbers: NaN and Inf
We have already run into two special numbers that can be generated by
arithmetic operations. Dividing a finite number by zero can lead to
an infinite "number" indicated by MATLAB as Inf . We get a
warning message when this occurs. It would be nice to be able to find
which element in an array took on such a value. Dividing 0 by 0 leads
to another special case: NaN (otherwise know as Not a Number.) Both
these special numbers can be seen in:
>> ex=[0 1 2]./[0 2 0]
Warning: Divide by zero
ex =
NaN 0.5000 Inf
The functions isnan , finite and isinf allow us to look for such special cases:
>> disp(isnan(ex))
1 0 0
>> disp(finite(ex))
0 1 0
>> disp(isinf(ex))
0 0 1
Note also that the logical operations work in a reasonable fashion with the exceptional numbers.
>> disp(ex==NaN)
0 0 0
>> disp(Inf>ex)
0 1 0
>> disp(Inf>=ex)
0 1 1
>> disp(NaN>ex)
0 0 0
>> disp(NaN>=ex)
0 0 0
>> disp(NaN==NaN)
0
The NaN value essentially can not be compared with any other
number, including itself . It is not equal to another copy of the
same thing, and it is not greater than or equal to another NaN. The
NaN value is unique in that it is the only value which is not equal
to itself.
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