francescoalemanno / fixedpoint.jl Goto Github PK

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Hi! Thanks for sharing this package, it's simple and effective!
I want to signal that the definition of tol as given in the readme is a bit misleading. The readme says

tol : absolute tolerance on |f(x)-x|

suggesting (at least to me) that if the algorithm converges (i.e. ends up using strictly less runs than the provided number of iters) the following inequality will always hold:

res = afps(f, x)
grad_norm( f( res.x ) - res.x ) < tol

This seems to be not always true.
The reason is that the update step is computed as

trial = x_n + β * v_n
g = f(trial) - trial
v_n = β * v_n + ϵ * g
x_n = x_n + v_n
runs += 1
if grad_norm(g) < tol
     break
end

and one sees that even if the iteration stops when grad_norm(f(trial) - trial) < tol, it is not x = trial that is returned, but x = trial + ϵ * g.

It may be that the current behaviour is the desired one, I just wanted to signal this in case it is not.

A modification of the update step satisfying the inequality above is

trial = x_n + β * v_n
g = f(trial) - trial
if grad_norm(g) < tol
    x_n = trial
    break
end
v_n = β * v_n + ϵ * g
x_n = x_n + v_n
runs += 1

(requiring also the initialisation runs = 1 I think).

hi, i saw your discourse post and then the repository and im really like it. On our package, we had to add a fixed point solver (just with damping) to solve some thermo problems: , but i would be glad to depend on an external package instead, specially if it provides convergence advantages over simple and damped fixed point iterations.

While the vector solver provided in this package is fine, it allocates a vector on each call. this will quickly becomes the main bottleneck. one idea is to provide an "implace" version of afps, afps! that accepts a function f!(out,x). then the function calls just overwrite a buffer vector instead of creating a new one.