TESTING/EIG/dget39.f(3)

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version 3.12.1 · 3 versions
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✨ NAME ✨

TESTING/EIG/dget39.f — bestie, this is the manual page from the Library Functions Manual for the DGET39 test routine. Periodt. 💅

🦋 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 🌸

Ok so DGET39 is literally the test for DLAQTR, which is the routine that solves 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'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  ]

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

Check the X matrix:

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. This is where the biggest ratio lands, bestie. 👑
  • LMAX — INTEGER. Example number where largest test ratio achieved. So you know which test case was the main character. 💅
  • NINFO — INTEGER. Number of examples where INFO is nonzero. Counts the messy ones. 😭
  • KNT — INTEGER. Total number of examples tested. The whole squad. 🫶

👑 Author 👑

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

Definition at line 102 of file dget39.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

And that's the whole vibe, bestie! 🌈 This page comes from LAPACK Version 3.12.0, and it's the manual for TESTING/EIG/dget39.f(3). Slay. 💖✨

📦 where this page comes from