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Reduce Logical Arrays to Single Value

Sometimes the result of a calculation produces an entire numeric or logical array when you need only a single logical true or false value. In this case, use the any or all functions to reduce the array to a single scalar logical for further computations.

The any and all functions are natural extensions of the logical | (OR) and & (AND) operators, respectively. However, rather than comparing just two elements, the any and all functions compare all of the elements in a particular dimension of an array. It is as if all of those elements are connected by & or | operators and the any or all functions evaluate the resulting long logical expression(s). Therefore, unlike the core logical operators, the any and all functions reduce the size of the array dimension that they operate on so that it has size 1. This enables the reduction of many logical values into a single logical condition.

First, create a matrix, A, that contains random integers between 1 and 25.

rng(0)
A = randi(25,5)
A =

    21     3     4     4    17
    23     7    25    11     1
     4    14    24    23    22
    23    24    13    20    24
    16    25    21    24    17

Next, use the mod function along with the logical NOT operator, ~, to determine which elements in A are even.

A = ~mod(A,2)
A =

     0     0     1     1     0
     0     0     0     0     0
     1     1     1     0     1
     0     1     0     1     1
     1     0     0     1     0

The resulting matrices have values of logical 1 (true) where an element is even, and logical 0 (false) where an element is odd.

Since the any and all functions reduce the dimension that they operate on to size 1, it normally takes two applications of one of the functions to reduce a 2–D matrix into a single logical condition, such as any(any(A)). However, if you use the notation A(:) to regard all of the elements of A as a single column vector, you can use any(A(:)) to get the same logical information without nesting the function calls.

Determine if any elements in A are even.

any(A(:))
ans =

     1

The result is logical 1 (true).

You can perform logical and relational comparisons within the function call to any or all. This makes it easy to quickly test an array for a variety of properties.

Determine if all elements in A are odd.

all(~A(:))
ans =

     0

The result is logical 0 (false).

Determine whether any main or super diagonal elements in A are even.

any(diag(A) | diag(A,1))
Error using  | 
Inputs must have the same size.

MATLAB returns an error since the vectors returned by diag(A) and diag(A,1) are not the same size.

To reduce each diagonal to a single scalar logical condition and allow logical short-circuiting, use the any function on each side of the short-circuit OR operator, ||.

any(diag(A)) || any(diag(A,1))
ans =

     1

The result is logical 1 (true). It no longer matters that diag(A) and diag(A,1) are not the same size.

See Also

| | | | |

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