# sggbal.f - Man Page

## 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.

**Date:**December 2016

**Further Details:**

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

Definition at line 179 of file sggbal.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sggbal(3) is an alias of sggbal.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK