not issue: a comment about complex ROTG in the BLAS

[langou]

This is not a bug, not an issue. We are just having a conversation about complex ROTG in the BLAS, and I want to document this conversation.

[C/Z]ROTG do not compute the output Z that [S/D]ROTG compute.

So [S/D]ROTG and [C/Z]ROTG differ in their semantics this way.

[ Jim Demmel ] Note that LAPACK SLARTG and CLARTG do not provide this capability of SROTG, so LAPACK doesn't need to have the output Z that [S/D]ROTG compute.

[ Sven Hammarling ] The original Level 1 BLAS did not have complex plane rotation routines, but there is no explanation as to why they were omitted. If we look at Table 1 (on p.310) in
"Basic Linear Algebra Subprograms for Fortran Usage" from Lawson, Hanson, Kincaid and Krogh in ACM Transactions on Mathematical Software, Volume 5, Issue 3, Sept. 1979, pp 308–323, https://doi.org/10.1145/355841.355847. We can see that it only names the D and S versions. The LINPACK Users' Guide mentions the addition of CSROT. LINPACK did not add complex plane rotation generation routines.

CROTG was then likely written for LAPACK and maybe the output Z was omitted because it wasn't needed.

Since nothing is broken, we don't see a reason to change the semantics of the interface of CROTG, which could inadvertently break something else.