Matrix-Free Linear Operator

[e-moral-sanchez]

This PR provides a MatrixFreeLinearOperator class which is a subclass of the abstract class LinearOperator.

The new class allows to create a general matrix-free linear operator. The constructor only requires the domain, codomain and a callable dot method.

Notes:

• the provided dot method may or may not take an 'out' argument
• a transpose_dot method may also be provided (mandatory to instantiate the transpose() linear operator)
• unit tests have been added

Additional change:

• in this PR we stop passing the deprecated tol argument in calls to scipy's minres. This forces us to use scipy >= 1.14 and hence python >= 3.9
• we also added a convergence verification in minres linear solver to avoid iterating when the initial solution is good enough (which may cause a division-by-zero error)

[campospinto]

This is useful I think, thanks!

As a test, you can check the behaviour of a "fake" matrix-free operator: an operator created with a dot product involving a Stencil Matrix should act exactly like the matrix itself.

You can also check that an iterative solver (like cg) can run with an object of this new class.

[campospinto]

I see that some tests are failing because of minres() getting an unexpected keyword argument tol. Is this related to this new class?

[e-moral-sanchez]

The new version 1.14.0 of SciPy removed the tol argument in minres: https://docs.scipy.org/doc/scipy-1.13.1/reference/generated/scipy.sparse.linalg.minres.html

This also affects PR https://github.com/campospinto/psydac_dev/pull/6 .

I will fix this in this PR.

[campospinto]

This PR provides the class MatrixFreeLinearOperator, which is a subclass of the abstract class LinearOperator.

The class MatrixFreeLinearOperator allows to create a general matrix-free linear operator. The constructor only requires the domain, codomain and a callable dot method.

TODO: add simple unit tests (ideas are welcome!)

I am just adding a few unit tests

[campospinto]

I am also adding some features to handle the case where the given dot method has not optional 'out' argument, and the possibility (not mandatory) to pass a 'transpose_dot' method