inpystem.tools.FISTA module

This module implements interfacing tools for the FISTA algorithm.

For further informations about the FISTA algorithm, have a look at 1.

1

BECK, Amir et TEBOULLE, Marc. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM journal on imaging sciences, 2009, vol. 2, no 1, p. 183-202.

class inpystem.tools.FISTA.FISTA(f, df, L, g, pg, shape, Nit=None, init=None, verbose=True)

Fast Iterative Shrinkage-Thresholding Algorithm implementation.

Variables

  • f (function) – \(C^{1,1}\) convex function.

  • df (function) – derivative function of f.

  • L (float) – Lipshitz contant of f.

  • g (function) – Non-smooth function.

  • pg (function) – g poximal operator.

  • shape (tuple) – The data shape.

  • Nit (None, int) – Number of iteration. If None, the iterations will stop as soon as the functional no longer evolve. Default is None.

  • init (numpy array) – Init point which shape is the same as the data. If None, a random initailization is drawn. Default is None.

  • verbose (bool) – If True, process informations are sent to the output. Default is True.

  • Nit_max (int) – Maximum number of iterations.

  • tau (float) – Descent step.

  • E (numpy array) – Functional evolution across iterations.

  • lim (float) – Controlls the stop condition in case Nit is None. The smallest lim, the more iterations before stopping. lim is usually 1e-4.

__init__(f, df, L, g, pg, shape, Nit=None, init=None, verbose=True)

Initialization function for FISTA.

Parameters

  • f (function) – \(C^{1,1}\) convex function.

  • df (function) – derivative function of f.

  • L (float) – Lipshitz contant of f.

  • g (function) – Non-smooth function.

  • pg (function) – g poximal operator.

  • shape (tuple) – The data shape.

  • Nit (None, int) – Number of iteration. If None, the iterations will stop as soon as the functional no longer evolve. Default is None.

  • init (numpy array) – Init point which shape is the same as the data. If None, a random initailization is drawn. Default is None.

  • verbose (bool) – If True, process informations are sent to the output. Default is True.

StopCritera(n)

This function computes a critera that informs about the algorithm convergence at step n.

Parameters

n (int) – Current step

Returns

Value of the critera.

Return type

float

StopTest(n)

This function choose if iterations should be stopped at step n. If Nit is not None, it returns True as long as n is smaller than Nit. If Nit is None, it returns True as long as the functional is evolving fast.

Parameters

n (int) – Current step.

Returns

Should the iterations go on ?

Return type

bool

execute()

Method that executes the FISTA algorithm.

Returns

  • numpy array – The optimum of the optimization problem.

  • dict – Extra informations about convergence.

Note

Infos in output dictionary:

  • E: Evolution of the functional along the iterations.

  • time: Execution time.