Refactor parallel communicators, Introduce module_parallel and migrate rhog_io to domain-aware interfaces - #7899

…n, ParaKmeshWorld

Step 1-2: establish module_parallel/ as the new home for parallel domain abstractions.

- ParaWorld: base class with tag + rank + size + comm, virtual destructor
  for polymorphism, protected constructors, make_serial factory for
  ParaCollection::add()
- ParaTag: 8 domain tag string constants (pw/kmesh/bsame_kdiff/bdiff_ksame/
  rgrid/diag/matrix/atom)
- ParaCollection: unique_ptr<ParaWorld> container with find(tag) and
  find_as<T>() for safe downcast; missing tag returns static empty domain
- ParaKmeshWorld: first domain subclass, extracts Parallel_Kpoints logic
  (k-point distribution, pool mapping, cross-pool collection, gather_kvec)
  into a self-contained class; tests only include para_kmesh_world.h
- All tests moved to module_parallel/test/ with both serial and MPI variants
- Old para_world tests in test/ and test_parallel/ removed
- CMakeLists.txt and Makefile.Objects updated

Extract pool-level parallel parameters (poolnproc, poolrank, npw, npw_per,
npwtot) from PW_Basis into a self-contained domain class. The actual
FFT-based distribution algorithm (method1/method2) stays in PW_Basis;
ParaPwWorld only holds the result: how many plane waves each process gets.

Tests only include para_pw_world.h, no PW_Basis or parallel_comm.h needed.

Extract DIAG_WORLD + GlobalV::DRANK/DSIZE/DCOLOR into a self-contained
domain class with drank()/dsize()/dcolor() aliases. Used by PEXSI
solver and LCAO HS IO modules.

Extract GRID_WORLD + GlobalV::GRANK/GSIZE + Parallel_Grid's
z-distribution tables (numz/startz/whichpro) into a self-contained
domain class. Owns grid dimensions and per-process z-plane allocation.

Cross-pool operations (reduce_across_pools, bcast, reduce) will be
added later with explicit communicator parameters, breaking the
cross-domain dependency on KP_WORLD/INT_BGROUP.

Extract INT_BGROUP + BP_WORLD + GlobalV::MY_BNDGROUP/NPROC_IN_BNDGROUP/
RANK_IN_BPGROUP into a self-contained domain class with both intra
and inter group communicators. Used by SDFT band parallel and BPCG
diagonalization.

Extract the process-grid part of Parallel_2D (dim0/dim1/coord) into a
self-contained domain class. The actual ScaLAPACK descriptor and BLACS
context management stay in Parallel_2D; this class only holds the
process grid dimensions and coordinates, computed automatically from
the communicator size.

Add para_comm.h/.cpp providing domain-aware communication primitives
(bcast, reduce, gather, min/max) that accept const ParaWorld& instead
of hardcoding MPI_COMM_WORLD or POOL_WORLD. Serial mode is a no-op
(except gather_int which copies locally). Invalid worlds are skipped.

Tests only need para_comm.h + para_world.h, no dependency on the old
parallel_common.h or parallel_reduce.h.

Add reduce_across_pools, bcast_data, and reduce_data methods to
ParaRgridWorld. These replace Parallel_Grid::reduce_across_pools,
Parallel_Grid::bcast, and Parallel_Grid::reduce respectively.

Key difference from old code: communicators are passed explicitly
as const ParaWorld& parameters, eliminating GlobalV::KPAR/MY_POOL/
RANK_IN_POOL and global POOL_WORLD/KP_WORLD/INT_BGROUP dependencies.

Serial mode: reduce_across_pools is no-op, bcast_data/reduce_data
copy local slabs directly. Invalid worlds are skipped safely.

Add para_setup.h/.cpp providing:
- divide_mpi_groups: utility to split nproc into num_groups (serial+MPI)
- split_pools: split WORLD into k-pools + band groups, returns ParaWorld
  objects for pw/kmesh/bsame_kdiff/bdiff_ksame domains
- split_diag_world: split for DIAG_WORLD
- split_grid_world: split for GRID_WORLD
- setup_para_worlds: top-level function assembling all 8 domains into
  a ParaCollection

Also adds make_mpi/make_mpi_ptr factory methods to ParaWorld for
constructing domains from MPI communicators (protected ctor stays
protected, factories are the public API).

Replaces Parallel_Global::divide_pools, split_diag_world,
split_grid_world, and divide_mpi_groups without touching old code.

The name "para_comm" was ambiguous (communicator? communication?).
Rename to para_mpi_func to match the file's role: a collection of
domain-aware MPI functions (bcast/reduce/gather/min/max).

Files renamed:
- para_comm.h/.cpp -> para_mpi_func.h/.cpp
- para_comm_test.cpp -> para_mpi_func_test.cpp
- para_comm_mpi_test.cpp/.sh -> para_mpi_func_mpi_test.cpp/.sh

Targets renamed accordingly (MODULE_BASE_para_mpi_func[_mpi]);
gtest suites renamed to ParaMpiFuncTest/ParaMpiFuncMpiTest.
No behavior change, 16/16 tests pass.

Add two top-level parallel domains for multi-image calculations
(e.g. NEB replicas with independent unit cells):

- para_esolver_world [color = image_id]: all processes of one
  esolver instance; every existing solver domain is now derived
  from it instead of being hard-wired to MPI_COMM_WORLD.
- para_images_world [color = rank_in_esolver]: cross-image
  communicator connecting corresponding ranks; MPI_COMM_NULL for
  nimage == 1 or uneven splits, following the KP_WORLD convention.

split_pools/split_diag_world/split_grid_world now take a parent
MPI_Comm, and setup_para_worlds takes nimage and builds the full
hierarchy: WORLD -> images split -> esolver domain -> kmesh/pw/
bgroup/diag/rgrid/matrix. The hierarchy tree is documented in
para_setup.h.

New MPI test (mpirun -np 4) verifies single-image degradation,
2-image split ranks/sizes, derived-domain sizes, and kpar=2 inside
images; multi-image tests skip under single-rank direct execution.

- Add explicit nspin parameter to read_rhog() signature, making it
  consistent with write_rhog() which already has nspin
- Remove #include of parameter.h and global_variable.h from rhog_io.cpp
  - No longer reads PARAM.inp.nspin anywhere
- Update charge_init.cpp call sites to pass the existing local nspin var
- Remove dead PARAM.input.nspin assignments and #define private public
  hack from read_rhog_test.cpp (rhog_io no longer consumes PARAM)

- PW_Basis* rhopw (new+delete) -> value member PW_Basis rhopw
- new complex*[1] + new complex[1471] (double-delete chain)
  -> vector<vector<complex>> rhog_data + vector<complex*> rhog
- Remove TearDown() entirely (RAII handles cleanup)
- Update call sites to use &rhopw and rhog.data()

- Add std::ostream* os_warning parameter to read_rhog() and write_rhog()
  (no default value; callers must pass explicitly)
- Replace ModuleBase::WARNING/WARNING_QUIT with a local warn() helper
  that writes to the injected stream on rank 0
- Remove indirect GlobalV dependencies: drop TITLE, timer, WARNING,
  WARNING_QUIT calls; drop timer.h include
- write_rhog: replace WARNING_QUIT with warn() + return false (same flow)
- Update all call sites to pass &GlobalV::ofs_warning:
  - charge_init.cpp (2 read_rhog calls)
  - esolver_fp.cpp (2 write_rhog calls)
  - read_rhog_test.cpp (4 read_rhog calls)
- read_rhog_test.cpp main(): replace GlobalV parallel vars with locals

…state

Move three file pairs from source_io/module_chgpot to source_estate root:
- rhog_io.h/cpp
- write_elecstat_pot.h/cpp
- write_init.h/cpp

Also migrate read_rhog_test.cpp to source_estate/test/.

Update all include paths, CMakeLists.txt (source_io and source_estate,
including test configs), and Makefile.Objects (OBJS_IO -> OBJS_SRCPW).

Add AGENTS.md rules 10-11: forbid #define private public access hacks
in new tests, and require test_<module>.cpp naming for new unit tests.

- Add 3 new tests: WriteRoundTrip, WriteFileFail, WriteRoundTripNspin2
  (write_rhog was previously 0% covered by tests)
- Add OsNullptrSilent test for nullptr warning stream safety
- Remove GlobalV::ofs_warning usage, use local std::ofstream + fixture helpers
- Extract setup_pw_basis() fixture method to avoid duplication

…ill, add input validation

- Rename namespace ModuleIO -> elecstate to match source_estate convention
  (rhog_io was the only source_estate file still using ModuleIO)
- Replace 3x ModuleBase::GlobalFunc::ZEROS with std::fill, remove
  global_function.h dependency, add <algorithm>
- Add defensive parameter checks at the top of read_rhog and write_rhog:
  - pw_basis null check
  - rhog null check
  - nspin range check (1-4)
  - read_rhog: nx/ny/nz > 0 check
- Update all call sites in esolver_fp.cpp, charge_init.cpp, test_rhog_io.cpp
- Update test expected warning strings to match new namespace