helper to generate linear operator refactoring

[duchesnay]

1) Harmonize linear operator construction helper: some helper return A, some return A, n_compact. Proposition all helper return only A

2) linear operator is actually a simple list. We would like to:

• store information like the Lipschitz constant (that could be computed only once and reused) and eventually the n_compacts
• Provide serialization to disk. This would also also a lot of computation time

I propose to create an object LinearOperator which is a list (inherits from a list) this way it will not impact the code. I propose to add, at least, 3 methods:

• L() return the Lipschitz constant, could be None
• load(filename): npz format not pickle !
• save(filename)

Question should we move from helper to statics constructors ?

[tomlof]

I totally agree with 1.

Point 2 seems like a good idea! Two comments:

• It is the Lipschitz constant of the gradient of the function that uses the linear operator that is considered. For A this means the largest squared singular value of A (largest eigenvalue of A'*A). This eigenvalue is then used in the computation of the Lipschitz constants, but this use is "unknown" from the point-of-view of the A matrix. Therefore, instead of L(), the function should be called sigma_max() or lambda_max(), or something like that.
• I think this class that inherits from list should be put in the existing module parsimony.utils.linalgs.

[duchesnay]

Totally agree with both comments, I am working on it

[duchesnay]

Point 1: harmonization is done commit: 0aebc160d5978d0d6637cef2a42278281beb16f6 Now working on point 2

[tomlof]

Perfect!

[duchesnay]

Done