SRC/zggbak.f(3)

SRC/zggbak.f(3) 🌈

Library Functions Manual — okay bestie, this is the page for SRC/zggbak.f, and it's lowkey a whole LAPACK moment. 💅

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NAME 🎀

SRC/zggbak.f

SYNOPSIS ✨

Functions/Subroutines 🦋

subroutine zggbak (job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)

ZGGBAK

Function/Subroutine Documentation 💖

subroutine zggbak (character job, character side, integer n, integer ilo,
     integer ihi, double precision, dimension( * ) lscale, double precision,
     dimension( * ) rscale, integer m, complex*16, dimension( ldv, * ) v,
     integer ldv, integer info)

ZGGBAK

Purpose 🔥

Okay so ZGGBAK forms the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by ZGGBAL. That's the vibe, and honestly it ate.

Parameters 👑

• JOB — JOB is CHARACTER*1. It specifies the type of backward transformation required:
  • = '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. JOB must be the same as the argument JOB supplied to ZGGBAL.
• 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.
• IHI — IHI is INTEGER. The integers ILO and IHI determined by ZGGBAL. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
• LSCALE — LSCALE is DOUBLE PRECISION array, dimension (N). Details of the permutations and/or scaling factors applied to the left side of A and B, as returned by ZGGBAL.
• RSCALE — RSCALE is DOUBLE PRECISION array, dimension (N). Details of the permutations and/or scaling factors applied to the right side of A and B, as returned by ZGGBAL.
• M — M is INTEGER. The number of columns of the matrix V. M >= 0.
• V — V is COMPLEX*16 array, dimension (LDV,M). On entry, the matrix of right or left eigenvectors to be transformed, as returned by ZTGEVC. On exit, V is overwritten by the transformed eigenvectors.
• LDV — LDV is INTEGER. The leading dimension of the matrix V. LDV >= max(1,N).
• INFO — INFO is INTEGER:
  • = 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 146 of file zggbak.f.

Author (auto-generated) 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie. Sign-off vibe: LAPACK, Version 3.12.0, page tag SRC/zggbak.f(3) — and there's no separate date line in this footer, so we're not inventing one. 💖✨