Loosen generic tensor operations to accept non-array operands#195
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## main #195 +/- ##
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Loosens the generic tensor operations (contraction, factorizations, matrix functions, permuted-add) to accept operands that are not `AbstractArray`s, so a backend can flow its own tensor type through the generic orchestration by overloading a small set of hooks rather than subtyping `AbstractArray`. The supporting refactors: - `matricize`/`unmatricize` split into permuting and non-permuting forms by name: the permuting forms are `matricizeperm`/`unmatricizeperm`/`unmatricizeperm!` (and `matricizeop` becomes `matricizeopperm`), while `unmatricize` is again the split-axes primitive `unmatricize(m, codomain_axes, domain_axes)`. Distinguishing the two resolves the method ambiguities that had forced the flattened signature and restores the split-axes call. - Output allocation goes through the bipartitioned `similar_map` hook instead of a flat `similar`, so a map-shaped backend can build its codomain and domain directly. - A private `PermutedDims` lazy-permutation wrapper mirrors `PermutedDimsArray` for non-array operands, letting a downstream `permuteddims` hand a lazily-permuted operand to `bipermutedimsopadd!`. The public `matricizeop` to `matricizeopperm` rename is breaking. The TensorKit backend that exercises these hooks lands in a follow-up PR.
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Summary
Loosens the generic tensor operations (contraction, factorizations, matrix functions, permuted-add) to accept operands that are not
AbstractArrays, so a backend can flow its own tensor type through the generic orchestration by overloading a small set of hooks rather than subtypingAbstractArray.The supporting refactors:
matricize/unmatricizesplit into permuting and non-permuting forms by name: the permuting forms arematricizeperm/unmatricizeperm/unmatricizeperm!(andmatricizeopbecomesmatricizeopperm), whileunmatricizeis again the split-axes primitiveunmatricize(m, codomain_axes, domain_axes). Distinguishing the two resolves the method ambiguities that had forced the flattened signature and restores the split-axes call.similar_maphook instead of a flatsimilar, so a map-shaped backend can build its codomain and domain directly.PermutedDimslazy-permutation wrapper mirrorsPermutedDimsArrayfor non-array operands, letting a downstreampermuteddimshand a lazily-permuted operand tobipermutedimsopadd!.The public
matricizeoptomatricizeoppermrename is breaking. The TensorKit backend that exercises these hooks lands in a follow-up PR.