Contents
dggbal - balance a pair of general real matrices (A,B)
SUBROUTINE DGGBAL(JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE,
WORK, INFO)
CHARACTER * 1 JOB
INTEGER N, LDA, LDB, ILO, IHI, INFO
DOUBLE PRECISION A(LDA,*), B(LDB,*), LSCALE(*), RSCALE(*),
WORK(*)
SUBROUTINE DGGBAL_64(JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE,
RSCALE, WORK, INFO)
CHARACTER * 1 JOB
INTEGER*8 N, LDA, LDB, ILO, IHI, INFO
DOUBLE PRECISION A(LDA,*), B(LDB,*), LSCALE(*), RSCALE(*),
WORK(*)
F95 INTERFACE
SUBROUTINE GGBAL(JOB, [N], A, [LDA], B, [LDB], ILO, IHI, LSCALE,
RSCALE, [WORK], [INFO])
CHARACTER(LEN=1) :: JOB
INTEGER :: N, LDA, LDB, ILO, IHI, INFO
REAL(8), DIMENSION(:) :: LSCALE, RSCALE, WORK
REAL(8), DIMENSION(:,:) :: A, B
SUBROUTINE GGBAL_64(JOB, [N], A, [LDA], B, [LDB], ILO, IHI, LSCALE,
RSCALE, [WORK], [INFO])
CHARACTER(LEN=1) :: JOB
INTEGER(8) :: N, LDA, LDB, ILO, IHI, INFO
REAL(8), DIMENSION(:) :: LSCALE, RSCALE, WORK
REAL(8), DIMENSION(:,:) :: A, B
C INTERFACE
#include <sunperf.h>
void dggbal(char job, int n, double *a, int lda, double *b,
int ldb, int *ilo, int *ihi, double *lscale, dou-
ble *rscale, int *info);
void dggbal_64(char job, long n, double *a, long lda, double
*b, long ldb, long *ilo, long *ihi, double
*lscale, double *rscale, long *info);
dggbal balances a pair of general real matrices (A,B). This
involves, first, permuting A and B by similarity transforma-
tions to isolate eigenvalues in the first 1 to ILO$-$1 and
last IHI+1 to N elements on the diagonal; and second, apply-
ing 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.
JOB (input)
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 (input) The order of the matrices A and B. N >= 0.
A (input/output)
On entry, the input matrix A. On exit, A is
overwritten by the balanced matrix. If JOB = 'N',
A is not referenced.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,N).
B (input) On entry, the input matrix B. On exit, B is
overwritten by the balanced matrix. If JOB = 'N',
B is not referenced.
LDB (input)
The leading dimension of the array B. LDB >=
max(1,N).
ILO (output)
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.
IHI (output)
See the description for ILO.
LSCALE (input)
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 (input)
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 (workspace)
dimension(6*N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value.
See R.C. WARD, Balancing the generalized eigenvalue problem,
SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.