📂Julia

How to Check if Elements of an Array Belong to a List in Julia

Guide ¹

julia> x = rand('a':'c', 10)
10-element Vector{Char}:
 'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)
 'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)
 'b': ASCII/Unicode U+0062 (category Ll: Letter, lowercase)
 'c': ASCII/Unicode U+0063 (category Ll: Letter, lowercase)
 'b': ASCII/Unicode U+0062 (category Ll: Letter, lowercase)
 'c': ASCII/Unicode U+0063 (category Ll: Letter, lowercase)
 'c': ASCII/Unicode U+0063 (category Ll: Letter, lowercase)
 'c': ASCII/Unicode U+0063 (category Ll: Letter, lowercase)
 'b': ASCII/Unicode U+0062 (category Ll: Letter, lowercase)
 'b': ASCII/Unicode U+0062 (category Ll: Letter, lowercase)

Let’s say we have an array as shown above. In the example, our goal is to select both 'a' and 'b'. Logically, one might think to broadcast with inclusion operator $\in$, but the result is as follows.

julia> x .∈ ['a', 'b']
ERROR: DimensionMismatch("arrays could not be broadcast to a common size; got a dimension with lengths 10 and 2")

A DimensionMismatch error was raised. This error occurred because broadcasting happened simultaneously to both the array x and the category ['a', 'b']. To interpret the error message, it’s confusing because the length 10 of x and the length 2 of ['a', 'b'] came in at the same time.

julia> x .∈ Ref(['a', 'b'])
10-element BitVector:
 1
 1
 1
 0
 1
 0
 0
 0
 1
 1

In this case, you can solve the broadcasting problem with the Ref() function. This allows 'a' and 'b' in ['a', 'b'] to be treated as scalars and find only the places with these two characters.

Precautions

julia> y = rand('a':'c', 1, 10)
1×10 Matrix{Char}:
 'b'  'a'  'b'  'b'  'a'  'c'  'a'  'b'  'b'  'c'

Consider the case of a $1 \times 10$ matrix as shown above. At first glance, it might seem no different from the case seen in the guide above, but .∈ is used in a completely different way.

julia> y .∈ ['a', 'b']
2×10 BitMatrix:
 0  1  0  0  1  0  1  0  0  0
 1  0  1  1  0  0  0  1  1  0

As you can see, the first row indicates the position of 'a', and the second row indicates the position of 'b'. This is due to the difference between a vector and a matrix.

julia> y .∈ Ref(['a', 'b'])
1×10 BitMatrix:
 1  1  1  1  1  0  1  1  1  0

Consistent results can be obtained when using Ref().

Environment

• OS: Windows
• julia: v1.7.0