Add preconditioning to the ALP CG solvers

[anyzelman]

Initial jab at adding standard preconditioning to the ALP CG. The following TODOs remain:

• [x] make sure this passes the regular tests for non-preconditioned CG;
• [x] add a smoke test for the preconditioned CG (e.g., simple Jacobi preconditioning);
• [x] expose the mechanism to the solver and ksolver transition paths.

(Note that the latter point corresponds to the actual feature request)

Bugfixes in this MR:

• the vector-to-vector foldr was not implemented in the BSP1D and hybrid backends, herewith fixed.
• the eWiseLambda for BSP1D and hybrid was using local indexing, while it should have been global.
• this also fixes a kind of meta-bug in the distributed implementation of grb::set(BSP1D,hybrid) that erroneously relied on local indexing

Tag @alberto-scolari

[anyzelman]

Optional feature: split preconditioners for use with ILU, I think @djelovina's use case was for that particular one, or does it make use of the standard preconditioning now provided (modulo testing)?

[anyzelman]

Current status: all passes, except preconditioned CG with bsp1d and hybrid backends due to a segfault. Given it only appears for the preconditioned case, the error should be rather isolated (perhaps it's in the build of the diagonal vector?)

[anyzelman]

Current status: all passes, except preconditioned CG with bsp1d and hybrid backends due to a segfault. Given it only appears for the preconditioned case, the error should be rather isolated (perhaps it's in the build of the diagonal vector?)

I suspect it's a global/local index translation issue -- the eWiseLambda on matrices gives back global indices (at least that's what's specified), while the bracket-operator may expect local indices (which would be an error). If this is indeed the case, then a second bugfix that would be piggy-backing on this MR is that eWiseLambda on vectors then apparently does not use global indices (for bsp1d and hybrid).

[anyzelman]

Retarget to v0.8 due to the bugfixes this MR contains

[anyzelman]

Running unit and smoke tests, then will move to the last TODO

[anyzelman]

All tests OK on x86 and ARM at this point

[anyzelman]

This one seems ready, I'll try to test the KML entry point manually (and will run automated tests simultaneously)

[anyzelman]

Manual test of entry point also passes. Waiting review/approve from @alberto-scolari before merge~

[anyzelman]

I'm happy again:) Concept release notes:

This MR resolves a feature request for a preconditioned CG accessible via a transition path. To enable this feature, this MR adds the following:

• standard left-sided preconditioning to the ALP CG has been added. There are now two entry points grb::algorithms::conjugate_gradient for non-preconditioned CG, and grb::algorithms::preconditioned_conjugate_gradient for PCG. They are kept separate since PCG requires one more work-space vector. The preconditioner is given as an std::function that returns a grb::RC, takes an output grb::Vector and an input const grb::Vector. Given it's an std::function, any state required by the preconditioner can be embedded into the function (there is no additional argument required for this).
• the sparse solver transition path API now can take preconditioners also. Since this is a C API, the preconditioner is given as a function pointer. The return type is an int where 0 indicates successful application of the preconditioner. The first argument is a raw output vector, the second a const input vector, and the third a void * argument to any state required by the preconditioner.
• the kml_iss.h transition path API now also takes preconditioners, given as a function pointer with signature according to the current KML solver specification.

The MR also expands and improves documentation regarding the transition path libraries.

This MR adds the following smoke test:

• preconditioned CG with simple Jacobi preconditioning, both for real (double) and the complex case. Note that for the complex case, Jacobi preconditioning may not be a good choice; it is not encouraged to use outside of smoke testing.

To enable the smoke tests, this MR additionally includes the following bugfixes:

• the vector-to-vector foldr was not implemented in the BSP1D and hybrid backends, herewith fixed;
• the eWiseLambda(vector) for BSP1D and hybrid was using local indexing, while it should have been global;
• a meta-bug in the distributed implementation of grb::set(BSP1D,hybrid) erroneously relied on local indexing of eWiseLambda.

As always and additionally, the MR include code style fixes in both related and unrelated files.

[anyzelman]

CI and tests OK