Fix #359: inv() skew guard only rejects rank-2 matrix products - #435
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is_provably_skew now matches only the skew() projection itself,
inner_product(P_skew, {3,4}, X, {1,2}) with rank-2 X, instead of any
contraction with P_skew on the left.
contains_skew_factor only recurses where det(M1·M2) = det(M1)·det(M2)
applies: tensor_mul chains whose children are all rank-2, and
single-index contractions of two rank-2 operands. inv(C:skew(A)) with
rank-4 C is generically invertible and no longer rejected.
Tests in TensorSpacePropagationTest: rank-4 contraction and other P_skew
contraction patterns are accepted, rank-2 products with a skew factor
are still rejected, and a numerical check confirms det(C:skew(A)) != 0,
P_skew{1,3}:A is not skew, and B·skew(A) is singular.
Signed-off-by: petlenz <peterlenz89.pl@gmail.com>
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Closes #359.
The
inv()singularity guard rejected operands that are generically invertible.is_provably_skewmatched anyinner_productwithP_skewon the left. It now requires the exactskew()projection:inner_product(P_skew, {3,4}, X, {1,2})with rank-2X(viaas_projector_contraction).inner_product(P_skew, {1,3}, X, {1,2})is not skew in general.contains_skew_factorrecursed through everytensor_mulandinner_product. The determinant argumentdet(M1·M2) = det(M1)·det(M2) = 0only holds for products of rank-2 matrices, so it now recurses only throughtensor_mulchains whose children are all rank-2, and single-index contractions of two rank-2 operands (a product of the operands or their transposes). Scalar multiples and negations are unchanged.inv(inner_product(C, {3,4}, skew(A), {1,2}))with rank-4Cis no longer rejected.inv()is the only caller of the classifier.Tests (
TensorSpacePropagationTest):InvAllowsRank4ContractionOfSkew:C4:skew(X)andC4:W(annotated skew) are accepted.SkewProjectorWithOtherIndicesIsNotSkew:P_skew{1,3}:Xis not classified skew andinvaccepts it.SkewClassificationMatchesNumerics: with random data in 3D,det(C4:skew(A)) != 0andinvevaluates to its inverse,P_skew{1,3}:Ais not skew,skew(A)is skew, andB·skew(A)andinner(B{1}, skew(A){2})are singular.InvRejectsMatrixProductsWithSkewFactor:skew(X),skew(X)·Band a single-index contraction withskew(X)are still rejected.Negative control: against the classifier on
main, the first three fail; the rejection test passes on both. No existing test encoded the over-general rejection. Full suite 2350/2350 (gcc-14 Debug,-Werrorexcept the pedantic/deprecated-declarations warnings already onmain).