SGET39(3)

💖 SGET39(3) — Library Functions Manual 💖

Okay bestie, welcome to the SGET39(3) page from the Library Functions Manual. This is not a drill: it's a Fortran test-routine page, and we're gonna make it make sense. 🫶✨

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/sget39.f

That's the name this page is carrying — yes, it's literally that full path. No nickname, no cute alias, just the file. 💅

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

subroutine SGET39 (rmax, lmax, ninfo, knt)
    SGET39

💅 Function/Subroutine Documentation 💅

🌈 subroutine SGET39 (real rmax, integer lmax, integer ninfo, integer knt) 🌈

SGET39

🎀 Purpose 🎀

Okay so SGET39 tests SLAQTR, which is the routine for solving the real or special complex quasi upper triangular system:

     op(T)*p = scale*c,
or
     op(T + iB)*(p+iq) = scale*(c+id),

...and it does all of that in real arithmetic. T is upper quasi-triangular. If it's complex, then the first diagonal block of T must be 1 by 1, and B has this special structure:

               B = [ b(1) b(2) ... b(n) ]
                   [       w            ]
                   [           w        ]
                   [              .     ]
                   [                 w  ]

Also, op(A) = A or A', where A' denotes the conjugate transpose of the matrix A.

On input, X = [ c ]. On output, X = [ p ]. The source lays it out like this:

On input, X = [ c ].  On output, X = [ p ].
              [ d ]                  [ q ]

Scale is an output less than or equal to 1, chosen to avoid overflow in X. This subroutine is specially designed for the condition number estimation in the eigenproblem routine STRSNA.

The test code verifies that the following residual is order 1:

     ||(T+i*B)*(x1+i*x2) - scale*(d1+i*d2)||
   -----------------------------------------
       max(ulp*(||T||+||B||)*(||x1||+||x2||),
           (||T||+||B||)*smlnum/ulp,
           smlnum)

(The (||T||+||B||)*smlnum/ulp term accounts for possible (gradual or nongradual) underflow in x1 and x2.) 🧚

🌸 Parameters 🌸

• RMAX — RMAX is REAL. Value of the largest test ratio.
• LMAX — LMAX is INTEGER. Example number where largest test ratio achieved.
• NINFO — NINFO is INTEGER. Number of examples where INFO is nonzero.
• KNT — KNT is INTEGER. Total number of examples tested.

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 102 of file sget39.f.

✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code.

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Okay that's the whole page, bestie. The footer info is LAPACK Version 3.12.0 and the source path on the footer is /home/abui...IG/sget39.f(3). There's no date in this footer, so that's the whole sign-off — no cap. 💖✨🎀