Add Tier-1 linear-algebra APIs: inv, lstsq, norm (v0.7.0) - #6
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- inv(A): matrix inverse via iterative-refinement solve(A, I) - lstsq(A, b): least squares via FP32 QR + augmented-system (Bjorck) refinement - norm(x, ord): vector/matrix norms; spectral norm via accurate Gram matrix - Wire exports, bump version to 0.7.0, add benchmarks/ci_tier1_validate.py - Validated on TPU v6e (inv/lstsq/norms ~1e-15); documented general-p norm TPU pow precision (~fp32) and set CI threshold accordingly
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Summary
Adds three composable linear-algebra routines on top of the accurate matmul/solve
core, completing the Tier-1 API surface and bumping the package to v0.7.0.
New APIs
inv(A)— matrix inverse via iterative-refinementsolve(A, I).lstsq(A, b)— least squares for full-rank overdetermined/squareA, using aone-time FP32 QR with augmented-system (Björck) iterative refinement. Refining the
residual alongside the solution reaches ~FP64 accuracy even when the least-squares
residual is large (plain residual refinement of the solution alone stalls near FP32 there).
norm(x, ord=...)— vector and matrix norms. Standard orders are exact FP64reductions; the matrix spectral norm (
ord=2) usessqrt(lambda_max(A^T A))from theaccurate Gram matrix.
Validation
CPU (
benchmarks/ci_tier1_validate.py) and on-device TPU v6e (v6e-1):inv: 8.3e-15lstsq: 1.4e-14 (refinement 3.4e-6 -> 1.4e-14)ci_cpu/ci_gram/ci_solvesuites: no regressionsKnown limitation
A general p-norm (p not in {1, 2, inf}) is computed as
(sum |x|^p)^(1/p); on TPU thex**p/**(1/p)transcendentals run at ~fp32 precision under emulated fp64 (~1e-8).Standard orders are unaffected. Documented in
norm()and the README.