This is 10x slower in Julia than in Python/Anaconda. Why?

tv_fista_demo.jl

function tv_fista(X::Array{Complex{Float64},2}; mu=0.1, niter=10)
  m, n = size(X);
  P = Any[zeros(Complex{Float64}, (m-1,n)), zeros(Complex{Float64}, (m,n-1))];
  R = Any[zeros(Complex{Float64}, (m-1,n)), zeros(Complex{Float64}, (m,n-1))];
  tk = 1;
  tkp1 = 1;
  D = zeros(Complex{Float64}, (m,n));
  fval = Inf;
  obj = zeros(niter);
  for t = 1:niter
    println("$t");
    fold = fval;
    Pold = P; # Computing the gradient of the objective function
    D = X - mu*Lforward(R);
    Q = Ltrans(D);
    # Taking a step towards minus of the gradient
    f = 0.125 / mu;
    P[2] = R[2] + f*Q[2];
    P[1] = R[1] + f*Q[1];

    # Peforming the projection step
    P[1] = projP(P[1]);
    P[2] = projP(P[2]);

    # Updating R and t
    tk = tkp1;
    tkp1 = (1.0 + sqrt(1.0 + 4.0*tk*tk)) ./ 2.0;
    f = (tk - 1.0)/tkp1;
    R[1] = P[1]*(1 + f) - f*Pold[1];
    R[2] = P[2]*(1 + f) - f*Pold[2];

    C = X - mu*Lforward(P);
    obj[t] = norm(C)^2;
  end
  X_den = D;
  return X_den, obj;
end

function projP(X::Array{Complex{Float64},2})
  m,n = size(X);
  for j = 1:n, i = 1:m
    if abs(X[i,j]) > 1.0
        X[i,j] /= abs(X[i,j]);
    end
  end
  return X;
end

function Lforward(P::Array{Any,1})
    m2, n2 = size(P[1]);
    m1, n1 = size(P[2]);
    if n2 != n1 + 1
        error("dimensions are not consistent");
    elseif m1 != m2 + 1
        error("dimensions are not consistent");
    end
    m = m2 + 1;
    n = n2;
    X = zeros(eltype(P[1]), (m, n));
    X[1:end-1,:] = P[1];
    X[:,1:end-1] = X[:,1:end-1] + P[2];
    X[2:end,:] = X[2:end,:] - P[1];
    X[:,2:end] = X[:,2:end] - P[2];
    return X;
end


Ltrans(X::Array{Complex{Float64},2}) =
    Any[X[1:end-1,:] - X[2:end,:], X[:,1:end-1] - X[:,2:end]];



# run a demo
n = 256;
X = complex(rand(n, n), rand(n, n));
@time Y, obj = tv_fista(X);

I tried to run the @time line two times on the bottom. From first to second, the timing went from 2.31 to 0.80 seconds, because the compilation only occurs on the first run in a session. This seems like cheating, but that 1.5 seconds does not increase when you increase the number of iterations.

I don't understand the code, but I also see that you use slicing a lot. Currently Julia takes a copy when slicing, and that might be different from what numpy does. One possibility might be to exchange some of the of them with calls to sub()

Thanks for the advice. I will give that a try.

What is the difference between slice and sub?

I don't appear to be able to assign to views of the array using slice and sub.

Currently, sub is the way to get around the copying of slices problem. This is one of the things that is planned for 0.3 - slices are views by default.

@davidsmith Would you be able to submit a PR to add this example to the julia perf benchmar?