modify xGBT02 and xGET02 to use 1-norm of op(A) not A (no.2 from PR #562)

[jip]

1. Comments improved, unified and fixed.
2. Code improved and fixed.

To unify with routines xGBT01, xGTT02, xLANGB, xTBT02, xTPT02, and xTRT02.

Some remarks:

1. It turned out that xLANGB, xLANGT, xLANTB, and xLANTP subroutines accept only a square matrix A, unlike xLANGE and xLANTR which allow A to be non-square.
2. xLANGB uses inline loop not SCSUM1/DZSUM1 for 1-norm and inf-norm computing.
3. xGET02 uses magnitude-based norms |y| unlike xGBT02 which uses taxicab-based norms |Re(y)| + |Im(y)|.

[codecov]

Codecov Report

Merging #571 (036ec87) into master (bd6add2) will not change coverage.
The diff coverage is n/a.

@@           Coverage Diff           @@
##           master     #571   +/-   ##
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  Coverage   82.37%   82.37%           
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  Files        1894     1894           
  Lines      190679   190679           
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  Hits       157065   157065           
  Misses      33614    33614           

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[langou]

xGET02 uses magnitude-based norms |y| unlike xGBT02 which uses taxicab-based norms |Re(y)| + |Im(y)|.

Good point. You are correct.

The fact that we use two different measures is awkward and I do not know why this has been like that.

I wonder whether using xLANGB in xGBT02 would not (1) simplify the code of xGBT02, and (2) use magnitude-based norms |y|.

[jip]

I wonder whether using xLANGB in xGBT02 would not (1) simplify the code of xGBT02, and (2) use magnitude-based norms |y|.

It would, but this change will require to extend xLANGB interface to accept non-square matrices. And also to extend xLANGT, xLANTB, and xLANTP in the same way, to maintain consistency.

[langou]

I see. Thanks @jip for explaining.

Another idea is to have SCASUM (and DZASUM) that works with complex ABS( z ) instead of ABS(REAL( z )) + ABS(IMAG( z )). Having such SCASUM and DZASUM could actually be useful for a variety of reason. Then we would simply replace the calls to SCASUM (and DZASUM) in CGBT02 (and ZGBT02) by these new routines.

So, well, I think that's great work @jip and we can leave it at that for now. And revisit as needed in the future.