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You can filter the elements of an array by applying one or more conditions to the array. For instance, if you want to examine only the even elements in a matrix, find the location of all 0s in a multidimensional array, or replace NaN values in a discrete set of data. You can perform these tasks using a combination of the relational and logical operators. The relational operators (>, <, >=, <=, ==, ~=) impose conditions on the array, and you can apply multiple conditions by connecting them with the logical operators and, or, and not, respectively denoted by &, |, and ~.

Apply a Single Condition

To apply a single condition, start by creating a 5-by-5 matrix, A, that contains random integers between 1 and 15.

rng(0)
A = randi(15,5)

A =

    13     2     3     3    10
    14     5    15     7     1
     2     9    15    14    13
    14    15     8    12    15
    10    15    13    15    11

Use the relational less than operator, <, to determine which elements of A are less than 9. Store the result in B.

B = A < 9

B =

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

The result is a logical matrix. Each value in B represents a logical 1 (true) or logical 0 (false) state to indicate whether the corresponding element of A fulfills the condition A < 9. For example, A(1,1) is 13, so B(1,1) is logical 0 (false). However, A(1,2) is 2, so B(1,2) is logical 1 (true).

Although B contains information about which elements in A are less than 9, it doesn't tell you what their values are. Rather than comparing the two matrices element by element, use B to index into A.

A(B)

ans =

     2
     2
     5
     3
     8
     3
     7
     1

The result is a column vector of the elements in A that are less than 9. Since B is a logical matrix, this operation is called logical indexing. In this case, the logical array being used as an index is the same size as the other array, but this is not a requirement. For more information, see Using Logicals in Array Indexing.

Some problems require information about the locations of the array elements that meet a condition rather than their actual values. In this example, use the find function to locate all of the elements in A less than 9.

I = find(A < 9)

I =

     3
     6
     7
    11
    14
    16
    17
    22

The result is a column vector of linear indices. Each index describes the location of an element in A that is less than 9, so in practice A(I) returns the same result as A(B). The difference is that A(B) uses logical indexing, whereas A(I) uses linear indexing.

Apply Multiple Conditions

You can use the logical and, or, and not operators to apply any number of conditions to an array; the number of conditions is not limited to one or two.

First, use the logical and operator, denoted &, to specify two conditions: the elements must be less than 9 AND greater than 2. Specify the conditions as a logical index to view the elements that satisfy both conditions.

A(A<9 & A>2)

ans =

     5
     3
     8
     3
     7

The result is a list of the elements in A that satisfy both conditions. Be sure to specify each condition with a separate statement connected by a logical operator. For example, you cannot specify the conditions above by A(2<A<9), since it evaluates to A(2<A | A<9).

Next, find the elements in A that are less than 9 AND even numbered.

A(A<9 & ~mod(A,2))

ans =

     2
     2
     8

The result is a list of all even elements in A that are less than 9. The use of the logical NOT operator, ~, converts the matrix mod(A,2) into a logical matrix, with a value of logical 1 (true) located where an element is evenly divisible by 2.

Finally, find the elements in A that are less than 9 AND even numbered AND not equal to 2.

A(A<9 & ~mod(A,2) & A~=2)

ans =

     8

The result, 8, is even, less than 9, and not equal to 2. It is the only element in A that satisfies all three conditions.

Use the find function to get the index of the 8 element that satisfies the conditions.

find(A<9 & ~mod(A,2) & A~=2)

ans =

    14

The result indicates that A(14) = 8.

Replace Values that Meet a Condition

Sometimes it is useful to simultaneously change the values of several existing array elements. Use logical indexing with a simple assignment statement to replace the values in an array that meet a condition.

Replace all values in A that are greater than 10 with the number 10.

A(A>10) = 10

A =

    10     2     3     3    10
    10     5    10     7     1
     2     9    10    10    10
    10    10     8    10    10
    10    10    10    10    10

A now has a maximum value of 10.

Replace all values in A that are not equal to 10 with a NaN value.

A(A~=10) = NaN

A =

    10   NaN   NaN   NaN    10
    10   NaN    10   NaN   NaN
   NaN   NaN    10    10    10
    10    10   NaN    10    10
    10    10    10    10    10

The resulting matrix has element values of 10 or NaN.

Replace all of the NaN values in A with zeros and apply the logical NOT operator, ~A.

A(isnan(A)) = 0;
C = ~A

C =

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

The resulting matrix has values of logical 1 (true) in place of the NaN values, and logical 0 (false) in place of the 10s. The logical NOT operation, ~A, converts the numeric array into a logical array such that A&C returns a matrix of logical 0 (false) values and A|C returns a matrix of logical 1 (true) values.