SRC/dggbal.f(3)

📦
version 3.12.1 · 4 versions
, in arch rolling

💅 NAME 💅

Okay bestie, welcome to SRC/dggbal.f(3) — yep, that's the page, and it lives in the Library Functions Manual. We're about to make matrix balancing make sense, no cap.

SRC/dggbal.f

✨ SYNOPSIS ✨

Under Functions/Subroutines you've got this iconic little signature:

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

🦋 Function/Subroutine Documentation 🦋

🫶 The signature, in full 🫶

subroutine dggbal (character job, integer n, double precision, dimension(
    lda, * ) a, integer lda, double precision, dimension( ldb, * ) b,
    integer ldb, integer ilo, integer ihi, double precision, dimension( * )
    lscale, double precision, dimension( * ) rscale, double precision,
    dimension( * ) work, integer info)
DGGBAL

🎯 Purpose 🎯

Okay so DGGBAL balances a pair of general real matrices (A,B). It's giving main-character energy for your generalized eigenvalue problem, fr fr.

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. Slay. ✨

🌸 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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:

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.

And yes, bestie, that formula block says LSCALE(j) inside the RSCALE description in the source — I'm keeping it exactly as written, no edits, no "fixing" the copy-paste moment 🫶

WORK

WORK is DOUBLE PRECISION 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 dggbal.f.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code.

That's the whole page, bestie 💖 — sourced from SRC/dggbal.f(3) and stamped LAPACK Version 3.12.0. The footer's date slot is giving empty, so no date to report — just vibes and balanced matrices ✨🦋

📦 where this page comes from