Add stdmult (#175)

This is the complement to `varmult`. Useful for finishing
JuliaImages/Images.jl#971

Author: timholy

src/ColorVectorSpace.jl

@@ -27,7 +27,7 @@ import SpecialFunctions: gamma, logabsgamma, lfact
 using Statistics
 import Statistics: middle # and `_mean_promote`
 
-export RGBRGB, complement, nan, dotc, dot, ⋅, hadamard, ⊙, tensor, ⊗, norm, varmult
+export RGBRGB, complement, nan, dotc, dot, ⋅, hadamard, ⊙, tensor, ⊗, norm, varmult, stdmult
 
 MathTypes{T,C<:Union{AbstractGray{T},AbstractRGB{T}}} = Union{C,TransparentColor{C,T}}
 
@@ -464,6 +464,14 @@ function varmult(op, itr; corrected::Bool=true, dims=:, mean=Statistics.mean(itr
     end
     return v / (corrected ? max(1, n-1) : max(1, n))
 end
+function stdmult(op, itr; kwargs...)
+    _sqrt(x::Real)        = sqrt(x)
+    _sqrt(c::Colorant)    = mapc(sqrt, c)
+    _sqrt(rgbrgb::RGBRGB) = RGBRGB(sqrt.(Matrix(rgbrgb)))
+
+    result = varmult(op, itr; kwargs...)
+    return isa(result, Union{Real,Colorant,RGBRGB}) ? _sqrt(result) : _sqrt.(result)
+end
 
 function __init__()
     if isdefined(Base, :Experimental) && isdefined(Base.Experimental, :register_error_hint)

test/runtests.jl

@@ -787,14 +787,23 @@ ColorTypes.comp2(c::RGBA32) = alpha(c)
         @test varmult(⋅, cs; mean=RGB(0, 0, 0)) ≈ (0.2^2+0.3^2+0.4^2 + 0.5^2+0.3^2+0.2^2)/3
         @test varmult(⊙, cs) ≈ 2*RGB(0.15^2, 0, 0.1^2)
         @test Matrix(varmult(⊗, cs)) ≈ 2*[0.15^2 0 -0.1*0.15; 0 0 0; -0.1*0.15 0 0.1^2]
+        @test stdmult(⋅, cs) ≈ sqrt(2*(0.15^2 + 0.1^2)/3)    # the /3 is for the 3 color channels, i.e., equivalence
+        @test stdmult(⋅, cs; corrected=false) ≈ sqrt((0.15^2 + 0.1^2)/3)
+        @test stdmult(⋅, cs; mean=RGB(0, 0, 0)) ≈ sqrt((0.2^2+0.3^2+0.4^2 + 0.5^2+0.3^2+0.2^2)/3)
+        @test stdmult(⊙, cs) ≈ RGB(sqrt(2*0.15^2), 0, sqrt(2*0.1^2))
+        @test_throws DomainError stdmult(⊗, cs)
 
         cs = [RGB(0.1, 0.2,  0.3)  RGB(0.3, 0.5, 0.3);
               RGB(0.2, 0.21, 0.33) RGB(0.4, 0.51, 0.33);
               RGB(0.3, 0.22, 0.36) RGB(0.5, 0.52, 0.36)]
         v1 = RGB(0.1^2, 0.15^2, 0)
+        s2v1 = mapc(sqrt, 2*v1)
         @test varmult(⊙, cs, dims=2) ≈ 2*[v1, v1, v1]
+        @test stdmult(⊙, cs, dims=2) ≈ [s2v1, s2v1, s2v1]
         v2 = RGB(0.1^2, 0.01^2, 0.03^2)
+        sv2 = mapc(sqrt, v2)
         @test varmult(⊙, cs, dims=1) ≈ [v2 v2]
+        @test stdmult(⊙, cs, dims=1) ≈ [sv2 sv2]
     end
 
     @testset "copy" begin