Rank-4 tensor_inv in scalar-arg diff visitor (#287) - #291
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The Magnus formula `d(C^{-1})/ds = -C^{-1} : (dC/ds) : C^{-1}` extends
naturally from rank 2 to rank 4 in the scalar-arg setting:
rank 2: -invA_{im} · dA_{mn} · invA_{nj}
two single-index contractions on (2)↔(1)
rank 4: -invA_{ijmn} · dA_{mnpq} · invA_{pqkl}
two two-index contractions on (3,4)↔(1,2)
Unlike the tensor-arg visitor — which has sym/skew/Magnus kernel
variants because differentiating w.r.t. a rank-2 X expands the rank —
the scalar-arg derivative dA/ds has the SAME rank as A, so the same
Magnus formula applies independent of algebraic class. The evaluator
dispatches on annotation at evaluation time via the inner tensor_inv's
space tag; the symbolic AST is the same either way.
Rank-2 path unchanged. Rank != 2 and != 4 keep the not_implemented
throw — the inv() factory rejects them already, so the visitor's guard
catches only direct `make_expression<tensor_inv>` constructions.
3 new tests in TensorDiffWrtScalarTest:
- InvRank4ZeroDerivativeWhenSIndependent — pass-5 singleton-aware
guard still fires (zero-suppression on s-independent inner).
- InvRank4ExercisedDirectly — non-zero diff path, rank/dim lock-in.
- InvRank3ThrowsNotImplemented — belt-and-braces guard.
The companion deferred case in #287 (non-integer / non-constant
tensor_pow exponent) remains blocked on tensor log() from #227.
Full suite: 1321/1321 passing (+3 from prior 1318).
Signed-off-by: petlenz <peterlenz89.pl@gmail.com>
Add the structural hash-equality lock-in the reviewer flagged as a
MEDIUM gap (`InvRank4StructuralLockIn`): rebuild the expected Magnus
formula `-invA : dA : invA` by hand and assert hash equality with the
visitor's output. This protects against silent reordering of the
contraction layout — e.g. swapping `{3,4}↔{1,2}` to `{1,2}↔{3,4}`,
both legal inner-product calls for unsymmetric inputs but producing a
structurally different AST. Numerical eval is intentionally NOT added
here: rank-4 `tmech::inv` requires the post-`db5d8aa` rewrite, which
is being enforced by parallel work in #289; once #289 lands the rank-4
inv eval becomes safe to lock numerically and we can add a separate
end-to-end test then.
The rank-3 wrapper-silence finding from the reviewer (`tensor_inv`
wrapper ctor accepts any rank, factory rejects only rank ∉ {2,4})
is filed as separate issue #292 — out of scope for this PR.
Full suite: 1322/1322 passing (+1 from prior 1321).
Signed-off-by: petlenz <peterlenz89.pl@gmail.com>
Signed-off-by: petlenz <peterlenz89.pl@gmail.com>
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Summary
Closes part of #287. The scalar-arg diff visitor (
tensor_differentiation_wrt_scalar) now handles rank-4tensor_invvia the symbolic Magnus formula:```
d(C^{-1})/ds = -C^{-1} : (dC/ds) : C^{-1}
```
The formula's shape doesn't change between rank 2 and rank 4 — only the contraction layout (1-index ↔ 2-index). Unlike the tensor-arg visitor, which needs separate sym/skew/Magnus kernel variants because differentiating w.r.t. a rank-2 X expands the rank, the scalar-arg derivative
dA/dshas the same rank asA, so the same formula applies regardless of algebraic class. The evaluator already dispatches on annotation at evaluation time via the innertensor_inv's space tag.What's NOT in this PR
The companion
tensor_powcase in #287 (non-integer / non-constant exponent) requireslog(A)for a tensorA, which is on the #227 wishlist. The throw remains; comment in the visitor body sharpened to point at #227.Test plan
TensorDiffWrtScalarTest.InvRank4ZeroDerivativeWhenSIndependent— singleton-aware zero-suppression still fires (parity with rank 2).TensorDiffWrtScalarTest.InvRank4ExercisedDirectly— non-zero diff path, rank/dim lock-in viamake_expression<tensor_inv>(s * D)to bypass theinv(α·A) → inv(A)/αfactory fold.TensorDiffWrtScalarTest.InvRank3ThrowsNotImplemented— belt-and-braces guard for directmake_expression<tensor_inv>constructions at unsupported rank.No numerical lock-in is added: rank-4
tmech::invrequires the post-Sep-2025inverse_wrapper_baserewrite which is being enforced by #289 (parallel work) — evaluating rank-4 inv against the stale system tmech would NaN. The tests verify structure (rank, dim, non-zero); end-to-end numerical verification rides on #289.