add methods for median and quantile with function as the first argument (#186)

Adds `quantile(f, v)` and `median(f, v)` methods, where `f` is a function,
and `v` is an abstract array.
Fixes #141, #27.

Author: ajinkya-k

src/Statistics.jl

@@ -904,6 +904,24 @@ _median(v::AbstractArray{T}, ::Colon) where {T} = median!(copyto!(Array{T,1}(und
 
 median(r::AbstractRange{<:Real}) = mean(r)
 
+"""
+    median(f, v)
+
+Apply the function `f` to each element of collection `v`
+and then compute the median.
+
+```jldoctest
+julia> using Statistics
+
+julia> median(√, [1, 3, 2])
+1.4142135623730951
+
+julia> median([√1, √3, √2])
+1.4142135623730951
+```
+"""
+median(f::Function, v) = median!(f.(v))
+
 """
     quantile!([q::AbstractArray, ] v::AbstractVector, p; sorted=false, alpha::Real=1.0, beta::Real=alpha)
 
@@ -1115,6 +1133,33 @@ julia> quantile(skipmissing([1, 10, missing]), 0.5)
 quantile(itr, p; sorted::Bool=false, alpha::Real=1.0, beta::Real=alpha) =
     quantile!(collect(itr), p, sorted=sorted, alpha=alpha, beta=beta)
 
+
+"""
+    quantile(f, v)
+
+Apply the function `f` to each element of collection `v`
+and then compute the quantile(s) at a specified probability
+or vector or tuple of probabilities `p` on the interval [0,1].
+
+```jldoctest
+julia> using Statistics
+
+julia> quantile(√, [1, 3, 2], 0.3)
+1.248528137423857
+
+julia> quantile([√1, √3, √2], 0.3)
+1.248528137423857
+
+julia> quantile(√, [1, 3, 2], (0.3, 0.4, 0.5))
+(1.248528137423857, 1.3313708498984762, 1.4142135623730951)
+
+julia> quantile(.√[1, 3, 2], (0.3, 0.4, 0.5))
+(1.248528137423857, 1.3313708498984762, 1.4142135623730951)
+```
+"""
+quantile(f::Function, v, p; sorted::Bool=false, alpha::Real=1.0, beta::Real=alpha) =
+    quantile!(f.(v), p; sorted=sorted, alpha=alpha, beta=beta)
+
 quantile(v::AbstractVector, p; sorted::Bool=false, alpha::Real=1.0, beta::Real=alpha) =
     quantile!(sorted ? v : Base.copymutable(v), p; sorted=sorted, alpha=alpha, beta=beta)
 

test/runtests.jl

@@ -836,6 +836,19 @@ end
     @test_throws InexactError quantile([DateTime(2023, 09, 02), DateTime(2023, 09, 03)], .1)
 end
 
+@testset "quantile and median with functions (issue #141, PR #186)" begin
+    xvec = [3, 1, 2, 4]
+    for p in (0.2, 0.5, 0.8)
+        @test quantile(√, xvec, p) ≈ quantile(.√xvec, p)
+        @test quantile(x -> x^2, xvec, p) ≈ quantile(xvec.^2, p)
+        @test median(√, xvec) ≈ median(.√xvec)
+        @test median(x -> x^2, xvec) ≈ median(xvec.^2)
+    end
+
+    y = rand(4)
+    @test all(quantile(√, y, (0.3, 0.4, 0.5)) .≈ quantile(.√y, (0.3, 0.4, 0.5)))
+end
+
 @testset "variance of complex arrays (#13309)" begin
     z = rand(ComplexF64, 10)
     @test var(z) ≈ invoke(var, Tuple{Any}, z) ≈ cov(z) ≈ var(z,dims=1)[1] ≈ sum(abs2, z .- mean(z))/9