dggbal-f(3)

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

 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 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,...,ILO-1 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,...,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 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,...,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 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 i-th 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), 141-152.

Definition at line 177 of file dggbal.f.

Author

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