SRC/dgebak.f(3)

🌸 SRC/dgebak.f(3) — like, the actual manual page for dgebak 🌸

okay bestie, so this is straight out of the Library Functions Manual and it's giving "BLAS/LAPACK internals, but make it readable" 💅. Sit down, grab a strawberry 🍓, and let's unbox what dgebak is actually doing, because it's lowkey iconic.

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✨ NAME ✨

SRC/dgebak.f — that's the file, that's the vibe. 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine dgebak (job, side, n, ilo, ihi, scale, m, v, ldv, info) — literally THE DGEBAK. main character energy fr fr 👑

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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 ✨ — yes that's the name, we're claiming it 🫶

🌈 Purpose (the whole point of her)

!> !> 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. !>

Translation, bestie: DGEBAL gave you a balanced matrix (it shuffled and rescaled things so the math behaved 🧚). DGEBAK is the glow-up reversal — it takes the eigenvectors you computed for that balanced version and undoes the permutation and/or scaling so they're eigenvectors of the original matrix again. no cap, that's it 💖

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🦋 Parameters 🦋

• JOB — JOB is CHARACTER*1

tells us what kind of backward transformation we're doing:

= '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.

⚠️ periodt: JOB must be the same as the argument JOB supplied to DGEBAL. like, they have to match. don't play with her.

• SIDE — SIDE is CHARACTER*1

= 'R':  V contains right eigenvectors;
= 'L':  V contains left eigenvectors.

pick a side, any side 😌

• N — N is INTEGER The number of rows of the matrix V. N >= 0. 🧮
• ILO — ILO is INTEGER (she's just an integer, but she matters, keep scrolling)
• 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. 👑 ikyk: those bounds are not a suggestion, they're a lifestyle.
• SCALE — SCALE is DOUBLE PRECISION array, dimension (N) Details of the permutation and scaling factors, as returned by DGEBAL. 🌸 this array is literally the recipe for undoing everything.
• 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.

🔥 heads up: V gets overwritten. on exit it's a whole new matrix. if you needed the old one… she's gone, sorry 😭

• LDV — LDV is INTEGER The leading dimension of the array V. LDV >= max(1,N). 🎀 classic Fortran leading-dimension moment.
• INFO — INFO is INTEGER

= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value.

so 0 is the slay, and anything negative means somebody handed over a bad argument 💀

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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 💜

Generated automatically by Doxygen for LAPACK from the source code.

(not a human, just a robot doing her little documentation dance 🤖✨)

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and that's the whole thing bestie, every flag, every bound, every "must be the same as", all of it 💅

🌈 this page is from LAPACK, Version 3.12.0, page SRC/dgebak.f(3). bye, drink water, and may all your INFO values be 0 🫶💖🎀