lib.utils

Collection of various utility functions supporting the main functionalities of the library.

lib.utils.afclean(fh)

Tries to purge an anonymous function of all non-essential workspace data.

Parameters: fh (function handle) – Input function handle to be cleansed.
Returns: fh_clean – The same as fh, but with its workspace reduced to the essential variables.
Return type: function handle

Example

>>> fh_clean = afclean(fh);

Note

Function retrieved from: Matt J (2021). Memory-efficient anonymous functions (https://www.mathworks.com/matlabcentral/fileexchange/45749-memory-efficient-anonymous-functions), MATLAB Central File Exchange. Retrieved October 17, 2021.

Warning

DISCLAIMERS (from the original author): The cleaning process will break anonymous functions that call nested functions or subfunctions. Unfortunately also, the implementation of AFCLEAN relies on a certain amount of undocumented MATLAB, in particular the FUNCTIONS command whose behavior in future releases of MATLAB, The MathWorks doesn’t guarantee. It also makes heavy use of EVAL. When the tool works, it seems to work well, but use at your own risk!

lib.utils.solver_find_elipse_point(y, pU, A, T, xsol, v2, W, epsilont, max_iterations, min_iterations, eps, use_fb, max_no_el)

Generate an initial point to initialize solver_proj_elipse_fb.

Parameters

y (cell{:} of complex[:]) – Input data. Each cell entry corresponds to a data block.
pU (cell{:} of double[:]) – Diagonal preconditioner (encoded as a vector) involved in the definition of the ellipsoid.
A (anonymous function) – Function handle representing the measurement operator.
T (cell{:} of double[:]) – Noise whitening diagonal matrices (encoded as vectors) associated with each data block. Each cell entry corresponds to a data block.
xsol (double[:, :]) – Inital image estimate.
v2 (cell{:} of complex[:]) – Data-fidelity dual variables associated with each data block.
W (cell{:} of bool[:]) – Cell of boolean vector indicating the global position of each data point in the full Fourier space (undo blocking).
epsilont (cell{:} of double) – Radius of the ellispoid.
max_iterations (int) – Maximum number of iterations.
min_iterations (int) – Minimum number of iterations.
eps (double) – Stopping criterion tolerance (relative variation in norm between two consecutive iterates).
use_fb (bool) – Flag to use a forward-backward algorithm.
max_no_el (int) – Maximum number of elements per block (?).

Returns

proj – Projection of the data y onto the ellipsoid considered.

Return type

double[:]

Note

Deprecated function, still used in [Onose2017], https://github.com/basp-group/SARA-PPD.

lib.utils.solver_proj_elipse_fb(v2, r2, y, U, epsilont, z0, max_itr, min_itr, eps)

Compute the projection of v2 + r2 onto the \(\ell_2\) ball centered in y, of radius epsilont with respect to the norm induced by the diagonal preconditioner U with the forward-backward algorithm.

Parameters

v2 (complex[:]) – Part of the input point to be projected onto the ellipsoid.
r2 (complex[:]) – Part of the input point to be projected onto the ellipsoid.
y (complex[:]) – Visibility vector, center of the \(\ell_2\) ball.
U (double[:]) – Diagonal preconditioning matrix (encoded as a vector).
epsilont (double) – Radius of the \(\ell_2\) ball.
z0 (complex[:]) – Algorithm starting point.
max_itr (int) – Maximum number of iterations.
min_itr (int) – Minimum number of iterations.
eps (double) – Stopping criterion tolerance (relative variation in norm between two consecutive iterates).

Returns

z (complex[:]) – Projection onto the ellipsoid.
k (int) – Number of iterations required to converge.

lib.utils.util_create_pool(NumWorkers)

Opens a new paralel pool with NumWorkers workers. If a similar pool already exists, keeps the existing pool.

Parameters: NumWorkers (int) – Numer of workers in the parallel pool.

lib.utils.util_divisor(n)

Provides a list of integer divisors of a number.

Parameters: n (int) – Input integer value.
Returns: d – Row vector of all distinct divisors of the positive integer n, including 1 and n.
Return type: int[1, :]

Example

>>> a = divisor(12);
>>> a = [1, 2, 3, 4, 6, 12];

Note

This function uses the default factor() routine in Matlab and hence is limited to input values up to \(2^{32}\). However if factor() routine does get updated for larger integers, this function will still work fine. Using factor() provides a significant speed improvement over manually seaching for the each divisor of n.
Author: Yash Kochar ( yashkochar@yahoo.com )
Last modified: 21st June 2009.