SRC/cggbal.f(3)

✨ NAME ✨

SRC/cggbal.f — live from the Library Functions Manual, and it's giving serious CGGBAL subroutine energy. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

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

CGGBAL — the main-character routine, bestie. 👑

✨ 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 — okay so this is the full signature, and yes, every single argument is here. 🫶

✨ Purpose ✨

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.

✨ 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

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.

✨ 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 175 of file cggbal.f.

✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code.

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💖 Final sign-off, bestie: LAPACK Version 3.12.0, source file SRC/cggbal.f(3) — and the footer date is literally not printed, so no made-up timestamp, periodt. 🍓🫶