
dggbal.f(3) LAPACK dggbal.f(3)
NAME
dggbal.f 
SYNOPSIS
Functions/Subroutines
subroutine dggbal (JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE, WORK, INFO)
DGGBAL
Function/Subroutine Documentation
subroutine dggbal (characterJOB, integerN, double precision, dimension( lda, * )A, integerLDA,
double precision, dimension( ldb, * )B, integerLDB, integerILO, integerIHI, double
precision, dimension( * )LSCALE, double precision, dimension( * )RSCALE, double precision,
dimension( * )WORK, integerINFO)
DGGBAL
Purpose:
DGGBAL 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.
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,...,ILO1 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,...,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.
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,...,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.
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 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 dggbal.f.
Author
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Version 3.4.2 Tue Sep 25 2012 dggbal.f(3) 
