sggbal(3P) Sun Performance Library sggbal(3P)NAMEsggbal - balance a pair of general real matrices (A,B)
SYNOPSIS
SUBROUTINE SGGBAL(JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE,
WORK, INFO)
CHARACTER * 1 JOB
INTEGER N, LDA, LDB, ILO, IHI, INFO
REAL A(LDA,*), B(LDB,*), LSCALE(*), RSCALE(*), WORK(*)
SUBROUTINE SGGBAL_64(JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE,
RSCALE, WORK, INFO)
CHARACTER * 1 JOB
INTEGER*8 N, LDA, LDB, ILO, IHI, INFO
REAL 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, DIMENSION(:) :: LSCALE, RSCALE, WORK
REAL, 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, DIMENSION(:) :: LSCALE, RSCALE, WORK
REAL, DIMENSION(:,:) :: A, B
C INTERFACE
#include <sunperf.h>
void sggbal(char job, int n, float *a, int lda, float *b, int ldb, int
*ilo, int *ihi, float *lscale, float *rscale, int *info);
void sggbal_64(char job, long n, float *a, long lda, float *b, long
ldb, long *ilo, long *ihi, float *lscale, float *rscale, long
*info);
PURPOSEsggbal balances a pair of general real matrices (A,B). This involves,
first, permuting A and B by similarity transformations to isolate ei‐
genvalues 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 accu‐
racy of the computed eigenvalues and/or eigenvectors in the generalized
eigenvalue problem A*x = lambda*B*x.
ARGUMENTS
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/output)
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 (output)
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 (output)
Details of the permutations and scaling factors applied to
the right side of A and B. If P(j) is the index of the col‐
umn interchanged with column j, and D(j) is the scaling fac‐
tor 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 illegal value.
FURTHER DETAILS
See R.C. WARD, Balancing the generalized eigenvalue problem,
SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
6 Mar 2009 sggbal(3P)
