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Block-tridiagonal Ops (glass::bdmv / glass::bdsv)

Single-block matrix-vector product for a block-tridiagonal matrix — the sparsity pattern of the KKT / Schur systems that arise in trajectory optimization and MPC. The matrix is stored as NumBlockRows contiguous BlockSize × (3·BlockSize) row-major strips laid out [L | D | R] (left / diagonal / right blocks), and the vectors use a padded layout (NumBlockRows + 2)·BlockSize (one BlockSize pad block on each end) so the edge block-rows need no special case — their absent L / R simply multiply the zero pad.

See :doc:`../user_guide/concepts/block_tridiagonal` for the layout in detail, and :doc:`pcg` for the conjugate-gradient solver built on top of this matvec.

.. doxygenfile:: src/base/banded/bdmv.cuh
   :no-link:

Direct solve (glass::bdsv)

Block-Cholesky (block-Thomas) direct factor + solve on the same strips — the exact one-sweep alternative to :doc:`pcg` for SPD block-tridiagonal systems: bdsv_factor (in place; MAIN ← Cholesky factor, LEFT ← coupling block), bdsv_solve (forward/backward block substitution, reusable per right-hand side), and the fused bdsv. Composed from potrf/trsm/syrk/gemv/trsv.

.. doxygenfile:: src/base/banded/bdsv.cuh
   :no-link:

Block accessors (store_block / load_block)

Strided read/write of a single BlockSize × BlockSize block into / out of a [L | D | R] strip (with an optional scale), used to assemble and unpack the block-tridiagonal strips. Block- and warp-scoped forms.

.. doxygenfile:: src/base/banded/block_access.cuh
   :no-link: