CGEBAK(3)

💅 CGEBAK(3) — like, the iconic eigenvector backward-transformation queen 👑

okay so bestie, you've wandered into the Library Functions Manual and honestly? you're in the right place. this page is all about CGEBAK — a subroutine from the LAPACK world, and it's giving backstage crew energy: it doesn't do the glamorous work, it fixes up the eigenvectors so they look right in the original matrix's outfit. periodt. 🎀

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cgebak.f — yes that's the whole name, she's got a long government name, it's fine, we still love her. 🫶

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🌸 SYNOPSIS 🌸

Functions/Subroutines

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

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🦋 Function/Subroutine Documentation 🦋

subroutine CGEBAK (character job, character side, integer n, integer ilo,
    integer ihi, real, dimension( * ) scale, integer m, complex, dimension(
    ldv, * ) v, integer ldv, integer info)

CGEBAK — the name, the legend, the function. 👑

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💜 Purpose 💜

CGEBAK forms the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by CGEBAL.

fr fr, that's the whole vibe: CGEBAL balanced your matrix (scaled and permuted her so the numbers behaved), and now CGEBAK takes the eigenvectors you got from that balanced version and undoes the balancing, so they're eigenvectors of your original matrix. it's the un-smoothing. the reverse glow-down. no cap. 🌈

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🎀 Parameters 🎀

JOB

JOB is CHARACTER*1

specifies the type of backward transformation required, bestie — pick your fighter:

• = 'N': do nothing, return immediately. (we love a low-effort icon 😌)
• = 'P': do backward transformation for permutation only
• = 'S': do backward transformation for scaling only
• = 'B': do backward transformations for both permutation and scaling

JOB must be the same as the argument JOB supplied to CGEBAL. like, match your receipts, okay? 💅

SIDE

SIDE is CHARACTER*1

• = 'R': V contains right eigenvectors
• = 'L': V contains left eigenvectors

left or right, she supports both. main character energy either way. 💖

N

N is INTEGER

the number of rows of the matrix V. N >= 0. yes, zero is allowed, we support the empty girls. 🧚

ILO

ILO is INTEGER

that's it. that's the whole description. she's mysterious like that. 🙈

IHI

IHI is INTEGER

the integers ILO and IHI determined by CGEBAL. specifically: 1 <= ILO <= IHI <= N, if N > 0; and ILO=1 and IHI=0, if N=0. so if N is zero, IHI is less than ILO — yes that looks wrong, no that's not wrong, it's just the special case, don't come for her. 💀

SCALE

SCALE is REAL array, dimension (N)

details of the permutation and scaling factors, as returned by CGEBAL. this is the lore. the receipts from the balancing step. 🍓

M

M is INTEGER

the number of columns of the matrix V. M >= 0. again, zero is valid, we don't judge. 🌸

V

V is COMPLEX array, dimension (LDV,M)

on entry, the matrix of right or left eigenvectors to be transformed, as returned by CHSEIN or CTREVC. on exit, V is overwritten by the transformed eigenvectors. so she does eat your input and replace it with a glow-up — that's not a bug, that's the whole job, bestie. 🔥

LDV

LDV is INTEGER

the leading dimension of the array V. LDV >= max(1,N). keep it legal or INFO will personally call you out. 💅

INFO

INFO is INTEGER

• = 0: successful exit — slay, we ate, no crumbs ✨
• < 0: if INFO = -i, the i-th argument had an illegal value

so a negative INFO literally points at which argument was being messy. it's a callout with a name attached. 😭

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👑 Author 👑

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

the whole squad collaborated on this one, and we thank them for their service. 🫶

Definition at line 129 of file cgebak.f. iykyk. 🦋

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⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. not a human, a machine, and honestly it did a great job, we stan automation. 🤖💖

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and that's the whole page, bestie! LAPACK, Version 3.12.0, from that cgebak.f(3) file — see you in the next manpage, mwah! 💋🎀🌈