How to solve a real vector

[MacroUniverse]

I understand the the generalized phase-retrieval problem solves |Ax| = b where both A and x are complex. But can phase-pack be used when A is complex and x is real?

[ZongyuLi-umich]

@tomgoldstein For the case that x is real, the gradient w.r.t. x should be real as well, and I don't think the current code
handle that case, e.g.,

%%  Define ingredients for FASTA
    % m x 1 -> 1 x 1
    % f(y) = .5 ||y - b||^2
    f = @(y) .5*norm(y(:)-b(:))^2;

    % m x 1 -> m x 1
    gradf = @(y) y(:)-b(:);

    % n x n -> 1 x 1
    % g(z) = mu||X||_nuc, plus characteristic function of the SDP cone
    g  = @(X) mu*norm(eig(X),1);
    
    % n x n -> n x n
    % proxg(z,t) = argmin t*mu*nuc(x)+.5||x-z||^2, with x in SDP cone
    proxg = @(X,t)  projectSemiDefCone(X, mu*t);