DGET39(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 DGET39(3) — Library Functions Manual 💖

This page is DGET39(3) from the Library Functions Manual; the header path stamp is /home/abui...IG/dget39.f(3). 🫶

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/dget39.f — literally the NAME entry, bestie. It's a path and it's iconic. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine DGET39 (rmax, lmax, ninfo, knt)
    DGET39

🦋 Function/Subroutine Documentation 🦋

subroutine DGET39 (double precision rmax, integer lmax, integer ninfo, integer knt)
    DGET39

💜 Purpose

Okay so DGET39 tests DLAQTR, 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),

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.

On input / output, the vector tea is exactly:

 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 DTRSNA.

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 — DOUBLE PRECISION. Value of the largest test ratio. 💅
  • LMAX — INTEGER. Example number where largest test ratio achieved.
  • NINFO — INTEGER. Number of examples where INFO is nonzero.
  • KNT — 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 dget39.f. — noted, bestie. ✨

📜 Author 📜

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That's the whole page, bestie. Footer tea: LAPACK Version 3.12.0, and the footer's date/stamp field is /home/abui...IG/dget39.f(3). 💖

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