Conversion to PETSc with complex

[e-moral-sanchez]

Fix the functions to cast Psydac format to PETSc format and back:

• Identify the correct installation procedure for PETSc and petsc4py;
• Make functions work on complex-valued vectors and matrices;
• Make functions work in the serial case (where comm=None);
• Add more extensive unit testing;
• Update unit test workflow;
• Update README file.

This allows the use of high-performance PETSc solvers:

• PETSc must be installed with the complex configuration (see the instructions in the README).
• StencilVector, BlockVector, StencilMatrix and BlockLinearOperator have a topetsc() method.
• The function petsc_to_psydac in psydac.linalg.utilities.py allows us to convert a PETSc.Vec object (for instance, the vector solution after solving a system with PETSc) back to Psydac StencilVector or BlockVector format.

How to use it:
Let A be a StencilMatrix or BlockLinearOperator and b a StencilVector. We want to solve Ax=b with PETSc CG:

from psydac.linalg.utilities import petsc_to_psydac
from petsc4py import PETSC

Ap = A.topetsc() #converts operator to PETSc.Mat format

bp = b.topetsc() #converts vector to PETSc.Vec format

x = bp.duplicate() #x will be both the initial guess and where the solution is stored.
# If we have a particular initial guess in Psydac format, just convert it to PETSc.Vec format x = x.topetsc()

ksp = PETSc.KSP() # create Krylov solver type object
ksp.create(comm=Ap.comm) # pass communicator from PETSc.Mat object
opts = PETSc.Options() # create object to pass options to solver
opts["ksp_type"] = "cg" # set type of solver ("gmres" is default)
opts["pc_type"] = "none" # set preconditioner
opts["ksp_rtol"] = 1e-13
opts["ksp_atol"] = 1e-13
ksp.setFromOptions() # pass options to solver ksp
ksp.setOperators(Ap) # set system matrix. Preconditioner can also be passed here

ksp.solve(bp, x) # solve system

sol = petsc_to_psydac(x, V.vector_space) # convert solution to Psydac StencilVector format

Note: With this PR, the conversion from PETSC format to StencilVector format is not efficient, see issue #389.

[yguclu]

Good job!