SGGBAL (3)  Linux Manuals
NAME
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 (characterJOB, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, integerILO, integerIHI, real, dimension( * )LSCALE, real, dimension( * )RSCALE, real, dimension( * )WORK, integerINFO)
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 1norm 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.
NN is INTEGER The order of the matrices A and B. N >= 0.
AA 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.
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
BB 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.
LDBLDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
ILOILO is INTEGER
IHIIHI 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,...,ILO1 or i = IHI+1,...,N. If JOB = 'N' or 'S', ILO = 1 and IHI = N.
LSCALELSCALE 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,...,ILO1 = 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 ILO1.
RSCALERSCALE 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,...,ILO1 = 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 ILO1.
WORKWORK 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'.
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value.
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 November 2011
Further Details:

See R.C. WARD, Balancing the generalized eigenvalue problem, SIAM J. Sci. Stat. Comp. 2 (1981), 141152.
Definition at line 177 of file sggbal.f.
Author
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