Feature/banded opt v1

[realbabilu]

Using banded_optimizationV1 snapshot for the current

It is meant to be replayed onto an older tree only after the LAPACK
refactoring stack is already in place.

This snapshot should be applied after:

baseline BLAS / SuperLU selection work
the large lapack_surgery patch
lapack_peel_off
this banded_optimizationV1
The important bit is step 3. This V1 snapshot assumes the post-lapack_peel_off
structure already exists, especially in the LAPACK-facing LINK3, SOLVE_GMN,
matrix-export, and output paths. Applying this snapshot before
lapack_peel_off is likely to produce mismatched call flow and confusing merge
conflicts.

See:

patch_order.md
This is not the original bare banded patch anymore. It is the stable
validation-passing state after the follow-up debugging needed to keep
test_banded.py green.

The frozen behavior is:

keep the original RCM-enabled banded path
keep banded storage and solver-dispatch diagnostics
allow KLL to stay on true banded Cholesky when it is a good fit
bypass banded for compact-band cases that are too expensive or nearly dense
rescue selected static cases to SuperLU when banded/dense factorization is
not appropriate
preserve historical bailout semantics where the validation suite explicitly
expects them
rescue problematic RMM solves in SOLVE_GMN
emit zero-valued MPCFORCES
export PL and array-format UL Matrix Market files
Main regression point:

MYSTRAN_Validation-main\test_banded.py
Frozen result:

0/2605 failed -> PASS
See:

[dev_docs/validation_resume.md)
[dev_docs/issues_and_decisions.md)
In the frozen validation snapshot:

true banded KLL path is still the default
SuperLU is used as a rescue path when:
compact-band storage is too expensive for the matrix shape
DPBTRF fails and the deck family is allowed to rescue
constraint-heavy decks need sparse robustness
dense fallback is not a good path
Approximate split from the unique decks recorded under
MYSTRAN_Validation-main\passed_banded:

total unique passing decks counted: 272
true banded KLL path: 260 decks = 95.59%
SuperLU fallback on KLL: 12 decks = 4.41%
So the stable V1 state is still overwhelmingly banded in practice, with sparse
rescue used only where needed.

This snapshot keeps the older imported banded files and also carries the
follow-up production files that actually define the stable V1 behavior:

Source\LK3\LINK3.f90
Source\LK2\LINK2.f90
Source\LK2\SOLVE_GMN.f90
Source\LK9\L92\OFP2.f90
Source\UTIL\WRITE_MATRIX_MARKET_VECTOR.f90
The older marker style
! --- BANDED_optimizisation -begin-- ! / ! --- BANDED_optimizisation -end-- !
is preserved where it already existed historically. For newer follow-up logic
that never had the old markers, the snippet notes in this snapshot use:

! --- banded_optimization_V1 begin --- !
! --- banded_optimization_V1 end --- !
See:

snippets_banded_optimizationV1.md

Skyline fallback was explored after this work, but it was intentionally
removed from the runtime path because it hurt validation robustness.

The frozen V1 runtime policy is therefore simple: if banded is too costly or
unsuitable, rescue to SuperLU.

It is meant to be replayed onto an older tree only after the LAPACK
refactoring stack is already in place.

This snapshot should be applied after:

baseline BLAS / SuperLU selection work
the large lapack_surgery patch
lapack_peel_off
this banded_optimizationV1
The important bit is step 3. This V1 snapshot assumes the post-lapack_peel_off
structure already exists, especially in the LAPACK-facing LINK3, SOLVE_GMN,
matrix-export, and output paths. Applying this snapshot before
lapack_peel_off is likely to produce mismatched call flow and confusing merge
conflicts.

See:

patch_order.md
This is not the original bare banded patch anymore. It is the stable
validation-passing state after the follow-up debugging needed to keep
test_banded.py green.

The frozen behavior is:

keep the original RCM-enabled banded path
keep banded storage and solver-dispatch diagnostics
allow KLL to stay on true banded Cholesky when it is a good fit
bypass banded for compact-band cases that are too expensive or nearly dense
rescue selected static cases to SuperLU when banded/dense factorization is
not appropriate
preserve historical bailout semantics where the validation suite explicitly
expects them
rescue problematic RMM solves in SOLVE_GMN
emit zero-valued MPCFORCES
export PL and array-format UL Matrix Market files
Main regression point:

MYSTRAN_Validation-main\test_banded.py
Frozen result:

0/2605 failed -> PASS
See:

validation_resume.md
issues_and_decisions.md
In the frozen validation snapshot:

true banded KLL path is still the default
SuperLU is used as a rescue path when:
compact-band storage is too expensive for the matrix shape
DPBTRF fails and the deck family is allowed to rescue
constraint-heavy decks need sparse robustness
dense fallback is not a good path
Approximate split from the unique decks recorded under
MYSTRAN_Validation-main\passed_banded:

total unique passing decks counted: 272
true banded KLL path: 260 decks = 95.59%
SuperLU fallback on KLL: 12 decks = 4.41%
So the stable V1 state is still overwhelmingly banded in practice, with sparse
rescue used only where needed.

This snapshot keeps the older imported banded files and also carries the
follow-up production files that actually define the stable V1 behavior:

Source\LK3\LINK3.f90
Source\LK2\LINK2.f90
Source\LK2\SOLVE_GMN.f90
Source\LK9\L92\OFP2.f90
Source\UTIL\WRITE_MATRIX_MARKET_VECTOR.f90
The older marker style
! --- BANDED_optimizisation -begin-- ! / ! --- BANDED_optimizisation -end-- !
is preserved where it already existed historically. For newer follow-up logic
that never had the old markers, the snippet notes in this snapshot use:

! --- banded_optimization_V1 begin --- !
! --- banded_optimization_V1 end --- !
See:

snippets_banded_optimizationV1.md

Skyline fallback was explored after this work, but it was intentionally
removed from the runtime path because it hurt validation robustness.

The frozen V1 runtime policy is therefore simple: if banded is too costly or
unsuitable, rescue to SuperLU.