TESTING/EIG/sget39.f(3)

✨ TESTING/EIG/sget39.f ✨

okay bestie, so this is a page from the Library Functions Manual (very demure, very mindful) and it's all about one little Fortran subroutine that tests another routine. it's giving "QA girly who takes her job very seriously" and honestly? we love her for it. 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine sget39 (rmax, lmax, ninfo, knt) — the whole vibe. this is the one. SGET39. iconic name, no notes. 🎀

💖 Function/Subroutine Documentation 💖

subroutine sget39 (real rmax, integer lmax, integer ninfo, integer knt)

SGET39 — she's the girl in the lab coat running the vibe check on SLAQTR, a routine for solving the real or special complex quasi upper triangular system. no cap. 🧪✨

🔥 Purpose:

like, the whole point, okay:

SGET39 tests SLAQTR, a 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),

in real arithmetic. T is upper quasi-triangular. 🦋

If it is complex, then the first diagonal block of T must be 1 by 1, and B has the special structure:

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

op(A) = A or A', where A' denotes the conjugate transpose of the matrix A. (periodt. don't @ me.)

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. (safety first bestie, overflow is NOT the moment. 💀)

This subroutine is specially designed for the condition number estimation in the eigenproblem routine STRSNA. iykyk. 👑

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. lowkey important, don't skip it 🫶)

🌈 Parameters

• RMAX

RMAX is REAL Value of the largest test ratio. (the biggest number in the group chat, essentially 🔥)

• LMAX

LMAX is INTEGER Example number where largest test ratio achieved. (she remembers WHERE the drama happened 💅)

• NINFO

NINFO is INTEGER Number of examples where INFO is nonzero. (tracking the little chaos gremlins 😭)

• KNT

KNT is INTEGER Total number of examples tested. (the full headcount of the attendance sheet ✨)

🎀 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

(we stan all of them, truly the founding mothers of the numerics girlies 🫶💜)

Definition at line 102 of file sget39.f. (go look, she's literally right there 🌸)

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👑 Author

Generated automatically by Doxygen for LAPACK from the source code. (not a human, not a vibe, just a doc generator doing its thing 🎀)

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and that's the whole page bestie!! no cap, you now know everything about sget39 and its little ecosystem. slay. 💖✨

LAPACK — Version 3.12.0 — TESTING/EIG/sget39.f(3) 🦋