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Split reflectorApply! into a dot-based and a loop-based kernel - #1735
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`reflectorApply!(x, τ, A)` was based on `dot` and `axpy!`, which do not treat the elements of `A` as opaque: for arrays of arrays, `dot` recurses into the elements. The computation is now carried out by one of two kernels, `reflectorApplyNumeric!` (the previous implementation) for numeric elements, and `reflectorApplyLoop!` with explicit loops otherwise. Packages may dispatch to either kernel for their own element types. With this, the packed `QR` solves and the multiplication by `QRPackedQ` work for right-hand sides with vector-valued elements. The padding in the wide QR solve is filled with `fill!`, since broadcasting an array-valued zero would recurse into it. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013rqqAa24hUALGk57NefU4G
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dkarrasch
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Co-authored-by: Daniel Karrasch <daniel.karrasch@posteo.de>
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…or-valued right-hand side These are the remaining paths through `ldiv`; the least-squares case is supported since #1735. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013rqqAa24hUALGk57NefU4G
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Follow-up to #1734. The left-applying
reflectorApply!(x, τ, A)useddotandaxpy!, so for arrays of arraysdotrecursed into the elements and the packedQRsolves failed for vector-valued right-hand sides. The computation is now carried out by one of two kernels:reflectorApplyNumeric!: the previousdot/axpy!implementation, used for numericxandA;reflectorApplyLoop!: explicit loops that only multiply the elements ofAby the entries ofxand byτ, used otherwise.reflectorApply!dispatches between them on the element types, and packages can add methods for their own types that dispatch to either kernel. The wide packed QR solve now fills its padding withfill!, since broadcasting an array-valued zero recurses into it as well. Numeric code paths are unchanged (timings ofqrfactUnblocked!and_lqmul!on master and this branch agree within noise).Tests: both kernels agree with each other and with the definition for
Float64,ComplexF64andQuaternionelements; a matrix ofSizedArrays is reflected componentwise; the@test_brokenfrom #1734 is replaced by solves andQ/Q'multiplications withSizedArrayright-hand sides for all three QR types, with square, tall and wide matrices, vector and matrix right-hand sides.Related: #904, #1114.
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