P1673: LWG review 2023/10/25

`matrix_one_norm`

Last week, we stopped after matrix_frob_norm and before matrix_one_norm.

Add Note for BLAS Standard function name, even though not in Reference BLAS.

(In theory, a user could have a matrix with a layout for which submdspan isn't defined.)

"28.9.13.13.2 One norm with default result type" doesn't have a stable name. Remove that heading and make this part of the whole section. (Christian already has that implemented in his branch.) Ditto for the "see-below" changes (delete "see-below" and just return auto); flatten those functions to one line (Christian already did).

`matrix_inf_norm`

Ditto.

[linalg.alg.blas2.gemv]

2.1: Do we always have the same names of A, x, y, and z, in (e.g.,) possibly-multiplyable(decltype(A), decltype(x), decltype(y))? Christian: Yes, that's the idea, though we should check.

Shorten Complexity wording in para 4. "A count of mdspan array accesses and arithmetic operations that is linear in x.extent(0) times A.extent(1)."

Delete "Overwriting matrix-vector product" and "Updating matrix-vector product" headers. Make those headers just a new paragraph underneath: "This function performs an overwriting matrix-vector product."

Para 1: Replace "in this section" with "in [linalg.algs.blas2.gemv]." (Also, it's a "subclause," not a "section.")

Example for GEMV: Change scaled_matvec_2 to scaled_transposed_matvec. Use * instead of "times" in the comment over the last function.

[linalg.algs.blas2.symv]

Change "in this section" to the stable name of the parent, as above.

Remove subheadings "Overwriting symmetric matrix-vector product" etc., as above.

Edit Complexity as above. "A count of ... x.extent(0) times A.extent(1)." Perhaps even just "O(x.extent(0) * A.extent(1))."

^^^ Generally change Complexity to use brief big-Oh notation. The Oh is curly, math font. Fix this generally.

Add a cross-reference to [linalg.general], that explains the Triangle template parameter. "This function performs an overwriting symmetric matrix-vector product accessing the elements specified by t ([linalg.general])."

[linalg.algs.blas2.hemv]

Analogous changes as above.

[linalg.algs.blas2.trmv]

Analogous changes as above.

"taking account of the Triangle and DiagonalStorage parameters ([linalg.general])."

Note: "... other ExecutionPolicy specific optimizations" (remove hyphen) -- [linalg.algs.blas2.trmv.in-place].

Stop before [linalg.algs.blas2.trsv].

Things to fix this time

[x] "in this section" -> "in [stable.name]"
[x] Complexity
[x] Remove section headers like "28.9.13.13.2 One norm with default result type" and make them a sentence in the section. (Christian already has that implemented in his branch.)
[ ] Ditto for the "see-below" changes (delete "see-below" and just return auto); flatten those functions to one line (Christian already did).
[x] Example for GEMV: Change scaled_matvec_2 to scaled_transposed_matvec. Use * instead of "times" in the comment over the last function.
[x] "This function performs an overwriting matrix-vector product [accessing the elements specified by t ([linalg.general])]."
[x] Note: "... other ExecutionPolicy specific optimizations" (remove hyphen) -- [linalg.algs.blas2.trmv.in-place].

Other things to fix

[ ] matrix_*_norm: Add Note for BLAS Standard function name, even though these functions are not in the Reference BLAS.
[ ] Dimension-checking for rank-2 updates and BLAS 2 functions
[ ] Packed layouts
[ ] layout_transpose(d) and transposed (haven't reviewed yet)

ORNL / cpp-proposals-pub