DGEBAK(3)

🦋 dgebak.f(3) — the DGEBAK glow-up page 💅

ok so this is a page out of the Library Functions Manual bestie, and the star of the show lives at this absolutely unhinged path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgebak.f

like... she's nested. she's in her build directory era. we respect it 🫶

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgebak.f — yes the whole path is the name, that's just how LAPACK doxygen rolls, no cap.

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine DGEBAK (job, side, n, ilo, ihi, scale, m, v, ldv, info)
    DGEBAK

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💖 Function/Subroutine Documentation 💖

subroutine DGEBAK (character job, character side, integer n, integer ilo,
    integer ihi, double precision, dimension( * ) scale, integer m, double
    precision, dimension( ldv, * ) v, integer ldv, integer info)
    DGEBAK

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🧚 Purpose 🧚

!> !> DGEBAK forms the right or left eigenvectors of a real general matrix !> by backward transformation on the computed eigenvectors of the !> balanced matrix output by DGEBAL. !>

so basically: DGEBAL balanced your matrix and handed you back eigenvectors of the balanced version, and DGEBAK is the one that un-balances them — backward transformation, she undoes the glow-up so you get eigenvectors of your original matrix. iconic teamwork honestly 💫

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🎀 Parameters 🎀

• JOB — JOB is CHARACTER*1. Tells her which kind of backward transformation you want, and it's giving very much a menu:
  • = 'N': do nothing, return immediately; (the "not me, not today" option 💀)
  • = 'P': do backward transformation for permutation only;
  • = 'S': do backward transformation for scaling only;
  • = 'B': do backward transformations for both permutation and scaling.

⚠️ fr fr important: JOB must be the same as the argument JOB supplied to DGEBAL. like they have to match, that's the vibe check.

• SIDE — SIDE is CHARACTER*1:
  • = 'R': V contains right eigenvectors;
  • = 'L': V contains left eigenvectors.
• N — N is INTEGER. The number of rows of the matrix V. N >= 0.
• ILO — ILO is INTEGER. (yes that's all it says here, she's mysterious)
• IHI — IHI is INTEGER. The integers ILO and IHI determined by DGEBAL. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
• SCALE — SCALE is DOUBLE PRECISION array, dimension (N). Details of the permutation and scaling factors, as returned by DGEBAL. she's literally the receipts 💅
• M — M is INTEGER. The number of columns of the matrix V. M >= 0.
• V — V is DOUBLE PRECISION array, dimension (LDV,M). On entry, the matrix of right or left eigenvectors to be transformed, as returned by DHSEIN or DTREVC. On exit, V is overwritten by the transformed eigenvectors. 🔥 so like, she does NOT preserve your input, she's a main character who rewrites the scene.
• LDV — LDV is INTEGER. The leading dimension of the array V. LDV >= max(1,N).
• INFO — INFO is INTEGER:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value. 😭 rude but fair.

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👑 Author 👑

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

Definition at line 128 of file dgebak.f.

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💜 Author (again, bestie) 💜

Generated automatically by Doxygen for LAPACK from the source code. yeah she's auto-generated and still ate. 💅

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🌈 sign-off 🌈

okay that's the whole page!! this is LAPACK Version 3.12.0, and the file path footer situation is that sad truncated /home/abui...RC/dgebak.f(3) — her full address wouldn't fit so they hit her with the ..., tragic honestly, but we love her anyway. 🍓🧚💜

go forth and un-balance those eigenvectors, bestie 🌟