# Elegant value classification following a set of rules

**URL:** <https://discourse.julialang.org/t/elegant-value-classification-following-a-set-of-rules/14329>\
**Category:** New to Julia\
**Created:** [August 30, 2018, 7:49pm UTC](https://discourse.julialang.org/t/elegant-value-classification-following-a-set-of-rules/14329 "2018-08-30T19:49:25Z")\
**Posts on this page:** 9\
**Page:** 1

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**Author:** ![DominiqueMakowski](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dominiquemakowski/32/51410_2.png) [@DominiqueMakowski](https://discourse.julialang.org/u/DominiqueMakowski)\
**Post date:** [August 30, 2018, 7:49pm UTC](https://discourse.julialang.org/t/elegant-value-classification-following-a-set-of-rules/14329/1 "2018-08-30T19:49:25Z")

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I have some text labels for different ranges.

For example, “A” if x between 0 and 1, “B” if x between 1 and 2 and “C” if else.

I would like to find a neat way to store such information. And then, have a function that would retrieve the label for a value of x.

I’ve tried with a dict:

```julia
d = Dict(
    "A" => 0,
    "B" => 1,
    "C" => 2,
    "D" => 3
    )

```

Then I managed to collect the keys and values, but something tells me this might not be the best way to do it.

Any ideas?

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**Author:** ![NiclasMattsson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/niclasmattsson/32/21988_2.png) [@NiclasMattsson](https://discourse.julialang.org/u/NiclasMattsson)\
**Post date:** [August 30, 2018, 8:25pm UTC](https://discourse.julialang.org/t/elegant-value-classification-following-a-set-of-rules/14329/2 "2018-08-30T20:25:31Z")

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You need to specify the problem more precisely. Just a few questions off the top of my head:

- Are floating point ranges allowed? Your example only has integers.
- Can there be gaps between the ranges? Can they overlap?
- Is there a rule for what happens at the boundaries/overlaps, or can you return an arbitrary adjacent range? For example, what should your function return given an input of exactly 1?
- Can the boundaries be hard-coded? If not, will they be supplied sorted?

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**Author:** ![DominiqueMakowski](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dominiquemakowski/32/51410_2.png) [@DominiqueMakowski](https://discourse.julialang.org/u/DominiqueMakowski)\
**Post date:** [August 30, 2018, 8:48pm UTC](https://discourse.julialang.org/t/elegant-value-classification-following-a-set-of-rules/14329/3 "2018-08-30T20:48:11Z")

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Some details:

- Type: yes there would be floats
- Coverage: no gaps nor overlap between ranges
- Boundaries: What happens at boundaries is a good question. I believe there could be a parameter indicating the “direction” of evaluation. For example, let’s imagine the boundaries are 0, 0.1, 0.3 and 0.5.
  - In “ascending” order it would be: `0 <= x < 0.1`; `0.1 <= x < 0.3`; `0.3 <= x < 0.5` and `x >= 0.5`
  - In “descending” order it would be: `0 < x <= 0.1`; `0.1 < x <= 0.3`; `0.3 < x <= 0.5` and `x > 0.5`

In fact, I would like to implement a system of using rules of thumb heuristics for metrics interpretation. For example, there is the infamous grid for Cohen’s _d_ (1999), proposing that 0-0.2 = “negligible”, 0.2-0.5 = “small”, 0.5-0.8 = “medium” and \>0.8 = “large”.  
I would like a system to conveniently store such grids (I thought of Dict at first) and a function taking a value and such “rule’s set” and returning the correct label.

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**Author:** ![NiclasMattsson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/niclasmattsson/32/21988_2.png) [@NiclasMattsson](https://discourse.julialang.org/u/NiclasMattsson)\
**Post date:** [August 30, 2018, 10:29pm UTC](https://discourse.julialang.org/t/elegant-value-classification-following-a-set-of-rules/14329/4 "2018-08-30T22:29:51Z")

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If you store labels and breakpoints as arrays then you can immediately take advantage of the `searchsortedlast()` function.

```julia
struct LabelledRanges{T<:Real}
	breakpoints::AbstractArray{T}
	labels::AbstractArray
	isdesc::Bool
end

function LabelledRanges(breakpoints, labels, isdesc=true)
    if length(breakpoints) != length(labels)-1
        error("There must be exactly one more label than breakpoints.")
    elseif !issorted(breakpoints)
        error("Breakpoints must be sorted.")
    else
        LabelledRanges(breakpoints, labels, isdesc)
    end
end

getlabel(x::Real, r::LabelledRanges) = r.labels[1+searchsortedlast(r.breakpoints, x, lt=(r.isdesc ? (<=) : (<)))]

```

Usage:

```julia
julia> lr = LabelledRanges([0.0,0.1,0.3,0.5], ["below","A","B","C","above"], true);

julia> lr2 = LabelledRanges([0.0,0.1,0.3,0.5], ["below","A","B","C","above"], false);

julia> xx = [-1.0, 0.0, 0.01, 0.09, 0.1, 0.11, 0.29, 0.30, 0.31, 0.49, 0.50, 0.51];

julia> [x [getlabel(x,lr) for x in xx] [getlabel(x,lr2) for x in xx]]
 -1.0 "below" "below"
  0.0 "below" "A"
  0.01 "A" "A"
  0.09 "A" "A"
  0.1 "A" "B"
  0.11 "B" "B"
  0.29 "B" "B"
  0.3 "B" "C"
  0.31 "C" "C"
  0.49 "C" "C"
  0.5 "C" "above"
  0.51 "above" "above"

```

You may prefer to have the “direction of evaluation” to be a parameter of the `getlabel()` function instead of a property of `LabelledRanges`. Both choices are defendable I think.

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<div class="post-metadata">

**Author:** ![pdeffebach](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/pdeffebach/32/10320_2.png) [@pdeffebach](https://discourse.julialang.org/u/pdeffebach)\
**Post date:** [August 30, 2018, 10:30pm UTC](https://discourse.julialang.org/t/elegant-value-classification-following-a-set-of-rules/14329/5 "2018-08-30T22:30:41Z")

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I think you want [Match.jl](https://github.com/kmsquire/Match.jl)

EDIT: I wrote an example I thought would work but it doesn’t work. But maybe this can be solved with Match.jl

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**Author:** ![Tamas\_Papp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tamas_papp/32/25949_2.png) [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Post date:** [August 31, 2018, 6:26am UTC](https://discourse.julialang.org/t/elegant-value-classification-following-a-set-of-rules/14329/6 "2018-08-31T06:26:38Z")

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This is called _binning_, and is used very frequently when discretizing data. Eg see this code for `StatsBase.Histogram`:

[https://github.com/JuliaStats/StatsBase.jl/blob/00b5d9912aa6599f2b07c390f4c7f5a097a70dee/src/hist.jl#L175-L186](https://github.com/JuliaStats/StatsBase.jl/blob/00b5d9912aa6599f2b07c390f4c7f5a097a70dee/src/hist.jl#L175-L186)

Perhaps it would be good to expose this intermediate step in `StatsBase`.

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<div class="post-metadata">

**Author:** ![yakir12](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/yakir12/32/297_2.png) [@yakir12](https://discourse.julialang.org/u/yakir12)\
**Post date:** [August 31, 2018, 6:43am UTC](https://discourse.julialang.org/t/elegant-value-classification-following-a-set-of-rules/14329/7 "2018-08-31T06:43:09Z")

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How about [GitHub - BioJulia/IntervalTrees.jl: A data structure for efficient manipulation of sets of intervals](https://github.com/BioJulia/IntervalTrees.jl) ?

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<div class="post-metadata">

**Author:** ![DominiqueMakowski](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dominiquemakowski/32/51410_2.png) [@DominiqueMakowski](https://discourse.julialang.org/u/DominiqueMakowski)\
**Post date:** [August 31, 2018, 6:51am UTC](https://discourse.julialang.org/t/elegant-value-classification-following-a-set-of-rules/14329/8 "2018-08-31T06:51:12Z")

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Thank you all for your propositions, it is awesome to see how helping the community is!

I think I will stick with @NiclasMattsson suggestion, which is quite simple, flexible as tailorcrafted for this task and doesn’t need additional dependencies. Moreover, I suppose it’s an efficient solution as it is based on vectors…

Thanks 🙂

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<div class="post-metadata">

**Author:** ![foobar\_lv2](https://avatars.discourse-cdn.com/v4/letter/f/ee59a6/32.png) [@foobar\_lv2](https://discourse.julialang.org/u/foobar_lv2)\
**Post date:** [August 31, 2018, 8:04am UTC](https://discourse.julialang.org/t/elegant-value-classification-following-a-set-of-rules/14329/9 "2018-08-31T08:04:55Z")

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As long as you know beforehand whether you need to deal with Int/Float32/Float64, I’d suggest storing the breakpoints all as left-open right-closed intervals, using `nextfloat` if necessary. That is, `[L,R]=(nextfloat(L),R]`, `(L,R)=(L,prevfloat(R)]`. For integers you need to add or subtract one. That way you avoid looking up `isdesc`.