SGGBAL(3)

okay bestie, this is sggbal.f(3) from the Library Functions Manual — manual name folded in at the top like a little name tag 🎀

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sggbal.f — that’s the file this page is about, bestie 🫶

✨ SYNOPSIS ✨

Functions/Subroutines:

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

🌸 Function/Subroutine Documentation 🌸

Here’s the full signature, character-for-character:

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

SGGBAL

🎀 Purpose 🎀

SGGBAL balances a pair of general real matrices (A,B). It’s giving two-step glow-up ✨

1. First, it permutes 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.
2. Second, it applies 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, bestie. Balancing may reduce the 1-norm of the matrices, and it can improve the accuracy of the computed eigenvalues and/or eigenvectors in the generalized eigenvalue problem A*x = lambda*B*x. slay for numerical stability 💅

🎀 Parameters 🎀

JOB

JOB is CHARACTER*1. It 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 REAL 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 REAL 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 (and yes, the original text literally says LSCALE(j) right here — keeping it exact, bestie):

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.

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 ⭐

Definition at line 175 of file sggbal.f.

💀 Author 💀

Generated automatically by Doxygen for LAPACK from the source code.

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