ggbak(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

🌸 NAME 🌸

okay bestie, welcome to ggbak(3) from the Library Functions Manual — the whole vibe here is ggbak: back-transform eigvec 💅✨

✨ SYNOPSIS ✨

🦋 Functions

  • cggbak — CGGBAK
  • dggbak — DGGBAK
  • sggbak — SGGBAK
  • zggbak — ZGGBAK

Exact signatures, copied character-for-character because we do not play with code blocks 😌:

subroutine cggbak (character job, character side, integer n, integer ilo,
       integer ihi, real, dimension( * ) lscale, real, dimension( * ) rscale,
       integer m, complex, dimension( ldv, * ) v, integer ldv, integer info)
       CGGBAK
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
subroutine sggbak (character job, character side, integer n, integer ilo,
       integer ihi, real, dimension( * ) lscale, real, dimension( * ) rscale,
       integer m, real, dimension( ldv, * ) v, integer ldv, integer info)
       SGGBAK
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

🦋 Detailed Description 🦋

bestie, this is the detailed-description zone — the actual function docs are right below, and they are giving organized academic realness 📚💖

📚 Function Documentation 📚

💖 subroutine cggbak — CGGBAK 💖

subroutine cggbak (character job, character side, integer n, integer ilo,
       integer ihi, real, dimension( * ) lscale, real, dimension( * ) rscale,
       integer m, complex, dimension( ldv, * ) v, integer ldv, integer info)
       CGGBAK

✨ Purpose

CGGBAK 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 CGGBAL. slay 💅

🎀 Parameters

JOB is CHARACTER*1 and 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 CGGBAL.

SIDE is CHARACTER*1:

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

N is INTEGER — the number of rows of the matrix V. N >= 0.

ILO is INTEGER.

IHI is INTEGER — the integers ILO and IHI determined by CGGBAL. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

LSCALE is REAL array, dimension (N) — details of the permutations and/or scaling factors applied to the left side of A and B, as returned by CGGBAL.

RSCALE is REAL array, dimension (N) — details of the permutations and/or scaling factors applied to the right side of A and B, as returned by CGGBAL.

M is INTEGER — the number of columns of the matrix V. M >= 0.

V is COMPLEX array, dimension (LDV,M). On entry, the matrix of right or left eigenvectors to be transformed, as returned by CTGEVC. On exit, V is overwritten by the transformed eigenvectors.

LDV is INTEGER — the leading dimension of the matrix V. LDV >= max(1,N).

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 cggbak.f.

💜 subroutine dggbak — DGGBAK 💜

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. iconic ✨

🎀 Parameters

JOB is CHARACTER*1 and 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 DGGBAL.

SIDE is CHARACTER*1:

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

N is INTEGER — the number of rows of the matrix V. N >= 0.

ILO is INTEGER.

IHI is INTEGER — the integers ILO and IHI determined by DGGBAL. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

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 DGGBAL.

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 DGGBAL.

M is INTEGER — the number of columns of the matrix V. M >= 0.

V is 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.

LDV is INTEGER — the leading dimension of the matrix V. LDV >= max(1,N).

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 145 of file dggbak.f.

🧚 subroutine sggbak — SGGBAK 🧚

subroutine sggbak (character job, character side, integer n, integer ilo,
       integer ihi, real, dimension( * ) lscale, real, dimension( * ) rscale,
       integer m, real, dimension( ldv, * ) v, integer ldv, integer info)
       SGGBAK

✨ Purpose

SGGBAK 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 SGGBAL. periodt 💅

🎀 Parameters

JOB is CHARACTER*1 and 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 SGGBAL.

SIDE is CHARACTER*1:

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

N is INTEGER — the number of rows of the matrix V. N >= 0.

ILO is INTEGER.

IHI is INTEGER — the integers ILO and IHI determined by SGGBAL. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

LSCALE is REAL array, dimension (N) — details of the permutations and/or scaling factors applied to the left side of A and B, as returned by SGGBAL.

RSCALE is REAL array, dimension (N) — details of the permutations and/or scaling factors applied to the right side of A and B, as returned by SGGBAL.

M is INTEGER — the number of columns of the matrix V. M >= 0.

V is REAL array, dimension (LDV,M). On entry, the matrix of right or left eigenvectors to be transformed, as returned by STGEVC. On exit, V is overwritten by the transformed eigenvectors.

LDV is INTEGER — the leading dimension of the matrix V. LDV >= max(1,N).

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 145 of file sggbak.f.

🦋 subroutine zggbak — ZGGBAK 🦋

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

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. literally iconic 🌈

🎀 Parameters

JOB

  • JOB — JOB is CHARACTER*1. 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 🌟

These are the geniuses behind it:

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

Further Details 🔎

okay, source tea time:

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) 🤖

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