By: Blog by Bogumił Kamiński

Re-posted from: https://bkamins.github.io/julialang/2023/04/14/isequal.html

Introduction

Today I want to discuss how values are tested for being equal in
functions provided by DataFrames.jl.

I already discussed the topic of equality testing in the past in
this post and this post and
explain it extensively in chapter 7 of my Julia for Data Analysis book.
However, the issue is still often raised by users, so I thought it is useful
to go back to it one more time.

The post was written under Julia 1.9.0-rc1, CategoricalArrays.jl 0.10.7 and DataFrames.jl 1.5.0.

Why equality testing is hard?

When users learn Julia they are typically taught that == is the operator
that should be used for testing for equality. Here is a basic example:

julia> 1 == 2
false

julia> 1 == 1
true

However, there are the following aspects of == that make it not intuitive
in some scenarios.

First is that == does not guarantee to return Bool value. The problem
is that if one of its arguments is missing then the result will be missing:

julia> 1 == missing
missing

julia> missing == missing
missing

Clearly this is not desirable in cases when we expect the operation to return Bool (e.g. when filtering data):

julia> x = [1, 2, missing, 4, 5]
5-element Vector{Union{Missing, Int64}}:
 1
 2
  missing
 4
 5

julia> x[x .> 2.5]
ERROR: ArgumentError: unable to check bounds for indices of type Missing

In such cases you should use the coalesce function to decide if you want to keep or drop missing values:

julia> x[coalesce.(x .> 2.5, false)]
2-element Vector{Union{Missing, Int64}}:
 4
 5

julia> x[coalesce.(x .> 2.5, true)]
3-element Vector{Union{Missing, Int64}}:
  missing
 4
 5

The second issue is that == follows IEEE semantics for floating-point numbers:

julia> NaN == NaN
false

julia> 0.0 == -0.0
true

First, you see that NaN is not considered to be equal to NaN. This can be quite surprising:

julia> x = [1, NaN, 2]
3-element Vector{Float64}:
   1.0
 NaN
   2.0

julia> x[x .== NaN]
Float64[]

instead the isnan function can be used:

julia> x[isnan.(x)]
1-element Vector{Float64}:
 NaN

The 0.0 and -0.0 case is even more tricky. These are two technically distinct values,
however, in some applications user might want them to be treated as equal, while in other
as not equal. IEEE standard determines that they are considered to be equal when compared
using ==.

In summary, the major problem with == is that it does not define a proper equivalence
relation. First, some values are not comparable (missing is returned); second
it is not reflexive (for NaN).

An alternative way to compare values

In many cases you need an equality operator that defines an equivalence relation.
In Julia this is provided by the isequal function. As you can read in its documentation:

isequal treats all floating-point NaN values as equal to each other,
treats -0.0 as unequal to 0.0, and missing as equal to missing.
Always returns a Bool value.

Let us check this:

julia> isequal(1, missing)
false

julia> isequal(missing, missing)
true

julia> isequal(NaN, NaN)
true

julia> isequal(0.0, -0.0)
false

In Julia functions that create equivalence classes over sets of some values use
isequal to test for equality. In Base Julia such are for example Dict and Set
operations or the unique function:

julia> Set([0.0, 0.0, -0.0, -0.0, NaN, NaN, missing, missing])
Set{Union{Missing, Float64}} with 4 elements:
  0.0
  NaN
  -0.0
  missing

julia> unique([0.0, 0.0, -0.0, -0.0, NaN, NaN, missing, missing])
4-element Vector{Union{Missing, Float64}}:
   0.0
  -0.0
 NaN
    missing

The same rules carry over to DataFrames.jl.

Testing for equality in DataFrames.jl

There are the following functionalities of DataFrames.jl that rely on the isequal equality test:

• deduplication with unique and related functions;
• grouping with groupby;
• joins (innerjoin etc.).

Let us see them in action one by one. We start with the deduplication:

julia> using DataFrames

julia> df = DataFrame(id=1:8, x=[0.0, 0.0, -0.0, -0.0, NaN, NaN, missing, missing])
8×2 DataFrame
 Row │ id     x
     │ Int64  Float64?
─────┼──────────────────
   1 │     1        0.0
   2 │     2        0.0
   3 │     3       -0.0
   4 │     4       -0.0
   5 │     5      NaN
   6 │     6      NaN
   7 │     7  missing
   8 │     8  missing

julia> unique(df, :x)
4×2 DataFrame
 Row │ id     x
     │ Int64  Float64?
─────┼──────────────────
   1 │     1        0.0
   2 │     3       -0.0
   3 │     5      NaN
   4 │     7  missing

Indeed, we see that 0.0 and -0.0 are considered as not equal,
while NaN and missing are deduplicated.

Now let us turn to grouping:

julia> show(groupby(df, :x), allgroups=true)
GroupedDataFrame with 4 groups based on key: x
Group 1 (2 rows): x = 0.0
 Row │ id     x
     │ Int64  Float64?
─────┼─────────────────
   1 │     1       0.0
   2 │     2       0.0
Group 2 (2 rows): x = -0.0
 Row │ id     x
     │ Int64  Float64?
─────┼─────────────────
   1 │     3      -0.0
   2 │     4      -0.0
Group 3 (2 rows): x = NaN
 Row │ id     x
     │ Int64  Float64?
─────┼─────────────────
   1 │     5       NaN
   2 │     6       NaN
Group 4 (2 rows): x = missing
 Row │ id     x
     │ Int64  Float64?
─────┼─────────────────
   1 │     7   missing
   2 │     8   missing

As you can see we get the same result again. As a side note let me
comment that unique internally uses the same mechanism as groupby
to identify duplicates.

Finally let us check joins:

julia> df_ref = DataFrame(x=[0.0, missing], val=1:2)
2×2 DataFrame
 Row │ x          val
     │ Float64?   Int64
─────┼──────────────────
   1 │       0.0      1
   2 │ missing        2

julia> outerjoin(df, df_ref, on=:x)
ERROR: ArgumentError: missing values in key columns are not allowed when matchmissing == :error

We get a first problem. Joins detect that missing value is present in key column.
By default it errors in such a case. We can change it using the matchmissing keyword argument.
Let us assume that we want missing values to be treated as equal and try the following join:

julia> outerjoin(df, df_ref, on=:x, matchmissing=:equal)
ERROR: ArgumentError: currently for numeric values NaN and `-0.0` in their real or imaginary components are not allowed. Use CategoricalArrays.jl to wrap these values in a CategoricalVector to perform the requested join.

We still get an error. In joins, for safety, if -0.0 is encountered in key then an error is thrown. This can be fixed by transforming the :x column to categorical,
in which case -0.0 and 0.0 are considered to be different:

julia> using CategoricalArrays

julia> outerjoin(transform(df, :x => categorical => :x), df_ref, on=:x, matchmissing=:equal)
8×3 DataFrame
 Row │ id      x          val
     │ Int64?  Float64?   Int64?
─────┼────────────────────────────
   1 │      1        0.0        1
   2 │      2        0.0        1
   3 │      7  missing          2
   4 │      8  missing          2
   5 │      3       -0.0  missing
   6 │      4       -0.0  missing
   7 │      5      NaN    missing
   8 │      6      NaN    missing

Let us check categorical vector in more detail:

julia> levels(categorical(df.x))
3-element Vector{Float64}:
  -0.0
   0.0
 NaN

As you can see 0.0 and -0.0 are considered to be separate levels in a categorical vector.

Conclusions

I hope the examples given today were useful for understanding how == and isequal work in Julia.

As a final comment let me add that throwing an error for joins on -0.0 was a decision that was made
for safety reasons. However, if users give us a feedback that adding other options of handling -0.0
would be useful (e.g. treating them as equal or not-equal) then we could consider adding this feature
in the future releases of DataFrames.jl.

By: Blog by Bogumił Kamiński

Re-posted from: https://bkamins.github.io/julialang/2023/04/07/narrowing.html

Introduction

Today I want to write about a topic that is a quite tricky
element of design of Julia. The issue is that it is sometimes hard
to predict the element type of the output collection produced by
an operation that transforms an input collection.

The description above looks complicated, but the problem is
encountered in practice, so let me explain it by example.

The post was written under Julia 1.9.0-rc1.

A basic example

Assume you have some input collection [1, 2, 3] and you
want to compute square root of all its elements.

Let us consider three standard ways how you can do it:

julia> x = [1, 2, 3]
3-element Vector{Int64}:
 1
 2
 3

julia> sqrt.(x)
3-element Vector{Float64}:
 1.0
 1.4142135623730951
 1.7320508075688772

julia> map(sqrt, x)
3-element Vector{Float64}:
 1.0
 1.4142135623730951
 1.7320508075688772

julia> [sqrt(v) for v in x]
3-element Vector{Float64}:
 1.0
 1.4142135623730951
 1.7320508075688772

As you can see in each case a proper element type, that is
Float64, was determined for the returned collection.

This behavior is useful, as the user does not have to think
about specifying the output element type. In fact,
in combination with the transformation using the identity function,
this behavior can be used to conveniently narrow
down element type of some collection:

julia> y = Any[1, 2, 3]
3-element Vector{Any}:
 1
 2
 3

julia> identity.(y)
3-element Vector{Int64}:
 1
 2
 3

julia> map(identity, y)
3-element Vector{Int64}:
 1
 2
 3

julia> [v for v in y]
3-element Vector{Int64}:
 1
 2
 3

This pattern comes handy if we have input data that does not have a known
element type, but later we want to perform element type narrowing
when processing it (one of the major benefits of such narrowing
is that processing vectors of Any values is slow so we typically want to avoid it).

The hard case

Automatic output element type detection works nice most of the time.
Unfortunately, when we work with empty collections, it becomes hard to predict.
Here is a simple example:

julia> String.([])
Any[]

julia> map(String, [])
String[]

julia> [String(v) for v in []]
Any[]

julia> string.([])
AbstractString[]

julia> map(string, [])
Any[]

julia> [string(v) for v in []]
Any[]

As you can see from it broadcating, map, and comprehension use a different set of
rules to automatically determine the produced element type. These rules of course
exist and could be learned, but the point is that the issue is non-trivial.

The problem is that when you are writing production code
(e.g. you are developing a package) you want to be sure
what the element type of the collection you produce will be, as often
you cannot know upfront if the input collection the user is going to provide
will be empty or not.

The solution I use

In situations when it matters what the element type of the collection
produced by some transformation is going to be I use comprehensions
with output element type annotation:

julia> [string(v) for v in []]
Any[]

julia> String[string(v) for v in []]
String[]

Such annotation has an additional consequence that it is going to perform
conversion of the produced elements to the target type if needed:

julia> using Test

julia> s = ["a", GenericString("a")]
2-element Vector{AbstractString}:
 "a"
 "a"

julia> [string(v) for v in s]
2-element Vector{AbstractString}:
 "a"
 "a"

julia> typeof.([string(v) for v in s])
2-element Vector{DataType}:
 String
 GenericString

julia> String[string(v) for v in s]
2-element Vector{String}:
 "a"
 "a"

julia> typeof.(String[string(v) for v in s])
2-element Vector{DataType}:
 String
 String

Note that in the example prefixing the comprehension with
String made sure that the result of the operation has
String element type and all produced values have this type.

Element type widening

Let me comment on one common related operation. What if we
want to initialize some container with a given value but
we want its element type to be wider? This is not an artificial
case – it often happens with missing (where we initialize
some container with this value only to later replace missing with proper
values).

Using the fill function is a first thing we might try:

julia> fill(missing, 3)
3-element Vector{Missing}:
 missing
 missing
 missing

However, the produced container has Missing element type which
is not useful if we e.g. wanted to later also store integers in it.

One can use a comprehension annotated with a proper output element type
instead:

julia> Union{Int, Missing}[missing for _ in 1:3]
3-element Vector{Union{Missing, Int64}}:
 missing
 missing
 missing

The pattern with missing is needed often enough that we have
a custom function in the Missings.jl package that can be used
to get the desired result more conveniently:

julia> using Missings

julia> missings(Int, 3)
3-element Vector{Union{Missing, Int64}}:
 missing
 missing
 missing

Conclusions

Fortunately, in interactive use the problem with setting
of the proper element type for some collection does not
occur often. However, when I write production programs I make
sure to always think if I need to use comprehension with
element type specification to ensure type stability of my code.