CGGBAL(3)

✨ NAME ✨

bestie, this whole page is literally cggbal.f(3) — that's the manual name 💅 — from the Library Functions Manual. The NAME line in the original is just the file path, and it's exactly:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cggbal.f

the header/footer tag path is /home/abui...RC/cggbal.f(3), iykyk. periodt. 🎀

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine CGGBAL (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info)
    CGGBAL

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💅 Function/Subroutine Documentation 💅

subroutine CGGBAL (character job, integer n, complex, dimension( lda, * ) a,
    integer lda, complex, dimension( ldb, * ) b, integer ldb, integer ilo,
    integer ihi, real, dimension( * ) lscale, real, dimension( * ) rscale,
    real, dimension( * ) work, integer info)
    CGGBAL

🌸 Purpose 🌸

okay so CGGBAL balances a pair of general complex matrices (A,B). This involves, first, permuting A and B by similarity transformations to isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N elements on the diagonal; and second, applying a diagonal similarity transformation to rows and columns ILO to IHI to make the rows and columns as close in norm as possible. Both steps are optional.

Balancing may reduce the 1-norm of the matrices, and improve the accuracy of the computed eigenvalues and/or eigenvectors in the generalized eigenvalue problem A*x = lambda*B*x.

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🌸 Parameters 🌸

• JOB — JOB is CHARACTER*1. Specifies the operations to be performed on A and B:
  • = 'N': none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0 and RSCALE(I) = 1.0 for i=1,...,N;
  • = 'P': permute only;
  • = 'S': scale only;
  • = 'B': both permute and scale.
• N — N is INTEGER. The order of the matrices A and B. N >= 0.
• A — A is COMPLEX array, dimension (LDA,N). On entry, the input matrix A. On exit, A is overwritten by the balanced matrix. If JOB = 'N', A is not referenced.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• B — B is COMPLEX array, dimension (LDB,N). On entry, the input matrix B. On exit, B is overwritten by the balanced matrix. If JOB = 'N', B is not referenced.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• ILO — ILO is INTEGER. that's the whole description, bestie. 🫶
• IHI — IHI is INTEGER. ILO and IHI are set to integers such that on exit A(i,j) = 0 and B(i,j) = 0 if i > j and j = 1,...,ILO-1 or i = IHI+1,...,N. If JOB = 'N' or 'S', ILO = 1 and IHI = N.
• LSCALE — LSCALE is REAL array, dimension (N). Details of the permutations and scaling factors applied to the left side of A and B. If P(j) is the index of the row interchanged with row j, and D(j) is the scaling factor applied to row j, then

LSCALE(j) = P(j)    for J = 1,...,ILO-1
          = D(j)    for J = ILO,...,IHI
          = P(j)    for J = IHI+1,...,N.

The order in which the interchanges are made is N to IHI+1, then 1 to ILO-1.

• RSCALE — RSCALE is REAL array, dimension (N). Details of the permutations and scaling factors applied to the right side of A and B. If P(j) is the index of the column interchanged with column j, and D(j) is the scaling factor applied to column j, then

RSCALE(j) = P(j)    for J = 1,...,ILO-1
          = D(j)    for J = ILO,...,IHI
          = P(j)    for J = IHI+1,...,N.

The order in which the interchanges are made is N to IHI+1, then 1 to ILO-1.

• WORK — WORK is REAL array, dimension (lwork). lwork must be at least max(1,6*N) when JOB = 'S' or 'B', and at least 1 when JOB = 'N' or 'P'.
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value.

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👑 Author 👑

the author squad is literally:

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

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🧚 Further Details 🧚

See R.C. WARD, Balancing the generalized eigenvalue problem, SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.

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Definition at line 175 of file cggbal.f.

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👑 Author (the Doxygen meta one) 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, this manual page is complete 💖 the footer vibe is LAPACK Version 3.12.0 plus /home/abui...RC/cggbal.f(3). no cap, that's the sign-off. mwah 💋