MATLAB®

Logical Classes

Overview

The logical data type represents a logical true or false state using the numbers 1 and 0, respectively. Certain MATLAB^® functions and operators return logical true or false to indicate whether a certain condition was found to be true or not. For example, the statement 50>40 returns a logical true value.

Logical data does not have to be scalar; MATLAB supports arrays of logical values as well. For example, the following statement returns a vector of logicals indicating false for the first two elements and true for the last three:

[30 40 50 60 70] > 40
ans =
     0     0     1     1     1

This statement returns a 4-by-4 array of logical values:

x = magic(4) >= 9
x =
     1     0     0     1
     0     1     1     0
     1     0     0     1
     0     1     1     0

The MATLAB functions that have names beginning with is (e.g., ischar, issparse) also return a logical value or array:

a = [2.5 6.7 9.2 inf 4.8];

isfinite(a)
ans =
     1     1     1     0     1

Logical arrays can also be sparse as long as they have no more than two dimensions:

x = sparse(magic(20) > 395)
x =
   (1,1)        1
   (1,4)        1
   (1,5)        1
  (20,18)       1
  (20,19)       1

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Identifying Logical Arrays

This table shows the commands you can use to determine whether or not an array x is logical. The last function listed, cellfun, operates on cell arrays, which you can read about in the section Cell Arrays.

Examples

Create a 3-by-6 array of logicals and use the whos function to identify the size, byte count, and class (i.e., data type) of the array.

rand('state',0);     % Initialize the state of the random number generator.
A = rand(3,6) > .5
A =
     1     0     0     0     1     0
     0     1     0     1     1     1
     1     1     1     1     0     1

whos A
  Name      Size            Bytes  Class      Attributes

  A         3x6                18  logical 

Find the class of each of these expressions:

B = logical(-2.8);  C = false;  D = 50>40;  E = isinteger(4.9);

whos B C D E
  Name      Size            Bytes  Class      Attributes

  B         1x1                 1  logical              
  C         1x1                 1  logical              
  D         1x1                 1  logical              
  E         1x1                 1  logical              

Display the class of A:

rand('state',0);     % Initialize the state of the random number generator.
A = rand(3,6) > .5

fprintf('A is a %s\n', class(A))
   A is a logical

Create cell array C and use islogical to identify the logical elements:

C = {1, 0, true, false, pi, A};
cellfun('islogical', C)
ans =
     0     0     1     1     0     1

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Functions that Return a Logical Result

This table shows some of the MATLAB operations that return a logical true or false. Most mathematics operations are not supported on logical values.

Examples

MATLAB functions that test the state of a variable or expression return a logical result:

A = isstrprop('abc123def', 'alpha')
A =
     1     1     1     0     0     0     1     1      1

Logical functions such as xor return a logical result:

xor([1 0 'ab' 2.4], [ 0 0 'ab', 0])
ans =
     1     0     0     1

Note however that the bitwise operators do not return a logical:

X = bitxor(3, 12);
whos X
  Name      Size            Bytes  Class     Attributes

  X         1x1                 8  double

String comparison functions also return a logical:

S = 'D:\matlab\mfiles\test19.m';
strncmp(S, 'D:\matlab', 9)
ans =
     1

Note the difference between the elementwise and short-circuit logical operators. Short-circuit operators, such as && and ||, test only as much of the input expression as necessary. In the second part of this example, it makes no difference that B is undefined because the state of A alone determines that the expression is false:

A = 0;
A & B
??? Undefined function or variable 'B'.

A && B
ans =
     0

One way of implementing an infinite loop is to use the while function along with the logical constant true:

while true
a = [];  b = [];
a = input('Enter username: ', 's');

   if ~isempty(a)
   b = input('Enter password: ', 's');
   end

   if ~isempty(b)
   disp 'Attempting to log in to account ...'
   break
   end
end

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Using Logical Arrays in Conditional Statements

Conditional statements are useful when you want to execute a block of code only when a certain condition is met. For example, the sprintf command shown below is valid only if str is a nonempty string:

str = input('Enter input string: ', 's');
if ~isempty(str) && ischar(str)
   sprintf('Input string is ''%s''', str)
end

Now run the code:

Enter input string: Hello
ans =
   Input string is 'Hello'

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Using Logical Arrays in Indexing

A logical matrix provides a different type of array indexing in MATLAB. While most indices are numeric, indicating a certain row or column number, logical indices are positional. That is, it is the position of each 1 in the logical matrix that determines which array element is being referred to.

See Using Logicals in Array Indexing for more information on this subject.

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Numeric Classes

Characters and Strings