[teeny] Reimplement the posdef matrix kernels on teeny (all 5 layouts)

[balbasty]

Part of the teeny refactor (umbrella fastfields-lib#21).

Replace the template-hack per-layout posdef kernels (posdef/{eye,diag,estatics,full}.inl + cholesky.h/utils.h machinery) with a single, readable posdef/matrix.h that expresses each per-voxel SPD layout on teeny views.

Scope

• One header posdef/matrix.h, namespaces ff::<FF_DEVICE>::posdef::{eye,diag,estatics,sym,full} + chol.
• All five packed layouts selected by packed length via guess_type(C, CC): Eye (CC=1), Diag (CC=C), ESTATICS (CC=2C-1), Sym (CC=C(C+1)/2, diag-then-rows), Full (CC=C²). The Eye>Diag>ESTATICS>Sym>Full priority is the efficiency order; collisions are exact equivalents (C=1: all layouts == a scalar; C=2: ESTATICS == Sym, same matrix + packing).
• Ops per layout: matvec / addmatvec_ / submatvec_ / matvec_backward (Sym) / solve(_) / invert(_), plus the Cholesky helpers with weighted-workspace variants for Sym/Full.

Numerics preserved

• reduce_t = double accumulation regardless of scalar_t (float/double), so mat-vec dot products and the Cholesky factorisation don't lose precision — mirrors jitfields.
• The 1.000001 diagonal ridge and 1e-40 pivot floor are carried over verbatim.

Gate

Validated bit-exactly against the old per-layout kernels and vs a brute-force double reference (fable review: 22,210 bit-exact old-vs-new checks + sanitizers, zero correctness bugs). The cpu-lib oracle (test_posdef.cpp) is the CI gate.

Part of fastfields-lib#21.

[balbasty]

Agent: claude-fastfields-to-teeny

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Generated by Claude Code

[balbasty]

Consolidation sweep (post repo-merge, 2026-08-20): done. include/fastfields/impl/kernels/posdef/matrix.h exists on current teeny with all 5 SPD layouts, consumed throughout the Phase B2 (posdef) tensor-native re-skin. Closing once the write endpoint's rate limit clears.

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Generated by Claude Code