---
name: "sggbal.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/sggbal.f"
---

# sggbal.f(3)

## NAME

SRC/sggbal.f

## SYNOPSIS

### Functions/Subroutines

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

## Function/Subroutine Documentation

### 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).  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 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
!>            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 **175** of file **sggbal.f**.

## Author

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