---
name: "cggbal"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/cggbal/3lapack"
---

# cggbal(3lapack)

balances a pair of general complex matrices (A,B)

## NAME

CGGBAL - balances a pair of general complex matrices (A,B)

## SYNOPSIS

- SUBROUTINE CGGBAL(

  JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE, WORK, INFO )

- CHARACTER

  JOB

- INTEGER

  IHI, ILO, INFO, LDA, LDB, N

- REAL

  LSCALE( \* ), RSCALE( \* ), WORK( \* )

- COMPLEX

  A( LDA, \* ), B( LDB, \* )

## 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.\

## ARGUMENTS

- JOB (input) 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 (input) INTEGER

  The order of the matrices A and B.  N \>= 0.

- A (input/output) 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 (input) INTEGER

  The leading dimension of the array A. LDA \>= max(1,N).

- B (input/output) 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 (input) INTEGER

  The leading dimension of the array B. LDB \>= max(1,N).

- ILO (output) INTEGER

  IHI     (output) 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 (output) 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 (output) 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 (workspace) 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 (output) INTEGER

  \= 0:  successful exit\
   \< 0:  if INFO = -i, the i-th argument had an illegal value.

## FURTHER DETAILS

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