Example of complex numbers with JuMP

complex-numbers-in-JuMP.jl

using JuMP

function Base.real{T <: JuMP.JuMPTypes}(x::Matrix{T})
    @assert size(x,1) == 2
    vec(x[1,:])
end
function Base.imag{T <: JuMP.JuMPTypes}(x::Matrix{T})
    @assert size(x,1) == 2
    vec(x[2,:]) 
end

function cmul{T <: JuMP.JuMPTypes}(z::Matrix{Complex128}, x::Matrix{T})
    ## `z` is a Matrix{Complex128} of size (N,N)
    ## `x` is a JuMP variable or AffExpr of size (2,N)
    ##     - the first row is the real component 
    ##     - the second row is the imaginary component 
    N = size(z, 1) 
    @assert size(x, 1) == 2
    @assert size(x, 2) == N
    res = Array(JuMP.GenericAffExpr{Float64, JuMP.Variable}, (2,N))
    res[1,:] = real(z) * real(x) - imag(z) * imag(x)
    res[2,:] = imag(z) * real(x) + real(z) * imag(x)
    res
end

m = Model()

@defVar(m, v1[1:2,1:3])
@defVar(m, v2[1:2,1:3])
@defVar(m, i[1:2,1:3])
z₁ = 3.0 + 6im
z₀ = 6.0 + 9im
Z = fill((z₀ - z₁)/3, 3, 3)
Z[1:4:9] = fill((z₀ + 2z₁)/3, 3) # diagonal

@addConstraint(m, cmul(Z, i) .== v1 - v2)

@addConstraint(m, v1 .== 10 * [2. -1     -1
                               0  -1.73   1.73])
@addConstraint(m, v2 .== 0.0)

solve(m)
iv = getValue(i)
I = reinterpret(Complex128, vec(iv))