SRC/dggbak.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

🦋 SRC/dggbak.f(3) — from the LAPACK Library Functions Manual 💅

okay bestie, buckle up, because this is the page for SRC/dggbak.f and honestly? it's a whole vibe. it's the backward-transformation girlie of the LAPACK fam and she deserves her moment. ✨

✨ NAME ✨

SRC/dggbak.f — bestie, that's it, that's the name. iconic of her, honestly. 🎀

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • subroutine dggbak (job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info) — the one and only DGGBAK, living her best life 💖

👑 Function/Subroutine Documentation 👑

🧚 subroutine dggbak (character job, character side, integer n, integer ilo, integer ihi, double precision, dimension( * ) lscale, double precision, dimension( * ) rscale, integer m, double precision, dimension( ldv, * ) v, integer ldv, integer info)

DGGBAK

🎯 Purpose:

!>
!> DGGBAK forms the right or left eigenvectors of a real generalized
!> eigenvalue problem A*x = lambda*B*x, by backward transformation on
!> the computed eigenvectors of the balanced pair of matrices output by
!> DGGBAL.
!>

like, literally what she does: you've got the real generalized eigenvalue problem A*x = lambda*B*x, and DGGBAK takes the eigenvectors that came out of DGGBAL's balanced pair and does the backward transformation on them so you get the right or left eigenvectors for real. no cap. 🔥

🌈 Parameters

  • JOB — CHARACTER*1, tells her what kind of backward transformation you want, and it must be the same as the argument JOB you supplied to DGGBAL (iykyk — mismatch and it's over for you 💀):
    • = 'N': do nothing, return immediately;
    • = 'P': do backward transformation for permutation only;
    • = 'S': do backward transformation for scaling only;
    • = 'B': do backward transformations for both permutation and scaling.
  • SIDE — CHARACTER*1, which flavour of eigenvectors you're holding:
    • = 'R': V contains right eigenvectors;
    • = 'L': V contains left eigenvectors.
  • N — INTEGER, the number of rows of the matrix V. N >= 0.
  • ILO — INTEGER. (that's the whole description bestie, she's mysterious 🫶)
  • IHI — INTEGER. ILO and IHI together are the integers determined by DGGBAL. Constraint era: 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
  • LSCALE — DOUBLE PRECISION array, dimension (N). The details of the permutations and/or scaling factors applied to the left side of A and B, as returned by DGGBAL.
  • RSCALE — DOUBLE PRECISION array, dimension (N). The details of the permutations and/or scaling factors applied to the right side of A and B, as returned by DGGBAL.
  • M — INTEGER, the number of columns of the matrix V. M >= 0.
  • V — DOUBLE PRECISION array, dimension (LDV,M). On entry: the matrix of right or left eigenvectors to be transformed, as returned by DTGEVC. On exit: V is overwritten by the transformed eigenvectors. she ate and left no crumbs 💅
  • LDV — INTEGER, the leading dimension of the matrix V. LDV >= max(1,N).
  • INFO — INTEGER, the receipts:
    • = 0: successful exit.
    • < 0: if INFO = -i, the i-th argument had an illegal value. 😭

💜 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🍓 Further Details:

!>
!>  See R.C. Ward, Balancing the generalized eigenvalue problem,
!>                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
!>

⭐ Definition at line 145 of file dggbak.f.

🎀 Author (the meta one) 🎀

Generated automatically by Doxygen for LAPACK from the source code. (yes she was birthed by a doc generator and she's still main character energy, we love that for her 🌸)

💖 cute little sign-off: this flawless creature is from LAPACK, Version 3.12.0, page SRC/dggbak.f(3). go forth, do your backward transformations, and slay. periodt. 🦋✨👑
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