SRC/sggbak.f(3)

🎀 SRC/sggbak.f(3) 🎀

okay bestie, welcome to the SRC/sggbak.f(3) page from the Library Functions Manual — and yes, it’s giving iconic LAPACK subroutine energy. Today’s main character is SGGBAK, and we’re gonna get you fully caught up. 💅✨

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✨ NAME ✨

SRC/sggbak.f

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🦋 SYNOPSIS 🦋

🌸 Functions/Subroutines 🌸

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

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💖 Function/Subroutine Documentation 💖

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. 👑🔥

🧚 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 SGGBAL. 🫶

• 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 SGGBAL. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. ✨
• LSCALE — 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 — 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 — M is INTEGER. The number of columns of the matrix V. M >= 0. 💖
• V — 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 — 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 145 of file sggbak.f.

🖨️ Author 🖨️

Generated automatically by Doxygen for LAPACK from the source code. 🫶

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byeee bestie 💜 — this page is from LAPACK, Version 3.12.0, for SRC/sggbak.f(3), and there’s no separate date listed in that footer, so consider this your cute little timestamp. 🎀🌈💅