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December 29, 2015 14:09
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This is 10x slower in Julia than in Python/Anaconda. Why?
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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); |
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?
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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()