Broadcasting issue with element-wise multiplication (Hadamard product)

[JinraeKim]

Issue

For now, Convex.jl does not support element-wise multiplication (that is, .*).
In many application cases, it is desirable that Convex.jl is compatible with such broadcasting & iterate methods.

It can be avoided by using dot(*)(x, y) (See operations table) but it's bit annoying when integrating Convex.jl with other-purpose applications.

Example codes

Here's the comparison:

1. with y = [6, 7, 8] (that is, an array)

function test()
    Wy = rand(128, 3)
    Wyu = rand(3, 5)
    by = rand(3)
    # y = Variable(3)
    y = [6, 7, 8]
    @bp
    result = Wy * (y .* (Wyu*zeros(5) .+ by))
end

@enter test()

Result:

1|julia> result
128-element Array{Float64,1}:
...

2. with y = Variable(3)

function test()
    Wy = rand(128, 3)
    Wyu = rand(3, 5)
    by = rand(3)
    y = Variable(3)
    # y = [6, 7, 8]
    @bp
    result = Wy * (y .* (Wyu*zeros(5) .+ by))
end

@enter test()

Result:

ERROR: MethodError: no method matching zero(::Convex.AdditionAtom)
Closest candidates are:
  zero(::Type{Pkg.Resolve.VersionWeight}) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.5/Pkg/src/Resolve/versionweights.jl:15
  zero(::Type{Pkg.Resolve.FieldValue}) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.5/Pkg/src/Resolve/fieldvalues.jl:38
  zero(::Type{ModelingToolkit.TermCombination}) at /home/jinrae/.julia/packages/ModelingToolkit/1qEYb/src/linearity.jl:67
  ...
Stacktrace:
 [1] generic_matvecmul!(::Array{Convex.AdditionAtom,1}, ::Char, ::Array{Float64,2}, ::Array{Convex.MultiplyAtom,1}, ::LinearAlgebra.MulAddMul{true,true,Bool,Bool}) at /home/jinrae/julia-1.5.3/share/julia/stdlib/v1.5/LinearAlgebra/src/matmul.jl:685
 [2] mul!(::Array{Convex.AdditionAtom,1}, ::Array{Float64,2}, ::Array{Convex.MultiplyAtom,1}, ::Bool, ::Bool) at /home/jinrae/julia-1.5.3/share/julia/stdlib/v1.5/LinearAlgebra/src/matmul.jl:81
 [3] mul!(::Array{Convex.AdditionAtom,1}, ::Array{Float64,2}, ::Array{Convex.MultiplyAtom,1}) at /home/jinrae/julia-1.5.3/share/julia/stdlib/v1.5/LinearAlgebra/src/matmul.jl:208
 [4] *(::Array{Float64,2}, ::Array{Convex.MultiplyAtom,1}) at /home/jinrae/julia-1.5.3/share/julia/stdlib/v1.5/LinearAlgebra/src/matmul.jl:51
 [5] test() at /home/jinrae/.julia/dev/GliderPathPlanning/test/icnn.jl:105

Note

• You can find the background of this issue in the post in JuliaLang.

[ericphanson]

Thanks very much for the issue. I had forgotten this before, but a similar issue came up before: #355. I think currently we support a few broadcasted operations, but not the full machinery of broadcasting. I think part of the issue there is that it can be difficult to implement performantly with Convex.jl's current design.

[odow]

Closing in favor of #479