cggbal(3P) Sun Performance Library cggbal(3P)NAMEcggbal - balance a pair of general complex matrices (A,B)
SYNOPSIS
SUBROUTINE CGGBAL(JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE,
WORK, INFO)
CHARACTER * 1 JOB
COMPLEX A(LDA,*), B(LDB,*)
INTEGER N, LDA, LDB, ILO, IHI, INFO
REAL LSCALE(*), RSCALE(*), WORK(*)
SUBROUTINE CGGBAL_64(JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE,
RSCALE, WORK, INFO)
CHARACTER * 1 JOB
COMPLEX A(LDA,*), B(LDB,*)
INTEGER*8 N, LDA, LDB, ILO, IHI, INFO
REAL LSCALE(*), RSCALE(*), WORK(*)
F95 INTERFACE
SUBROUTINE GGBAL(JOB, [N], A, [LDA], B, [LDB], ILO, IHI, LSCALE,
RSCALE, [WORK], [INFO])
CHARACTER(LEN=1) :: JOB
COMPLEX, DIMENSION(:,:) :: A, B
INTEGER :: N, LDA, LDB, ILO, IHI, INFO
REAL, DIMENSION(:) :: LSCALE, RSCALE, WORK
SUBROUTINE GGBAL_64(JOB, [N], A, [LDA], B, [LDB], ILO, IHI, LSCALE,
RSCALE, [WORK], [INFO])
CHARACTER(LEN=1) :: JOB
COMPLEX, DIMENSION(:,:) :: A, B
INTEGER(8) :: N, LDA, LDB, ILO, IHI, INFO
REAL, DIMENSION(:) :: LSCALE, RSCALE, WORK
C INTERFACE
#include <sunperf.h>
void cggbal(char job, int n, complex *a, int lda, complex *b, int ldb,
int *ilo, int *ihi, float *lscale, float *rscale, int *info);
void cggbal_64(char job, long n, complex *a, long lda, complex *b, long
ldb, long *ilo, long *ihi, float *lscale, float *rscale, long
*info);
PURPOSEcggbal balances a pair of general complex 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 ele‐
ments on the diagonal; and second, applying a diagonal similarity
transformation to rows and columns ILO to IHI to make the rows and col‐
umns 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)
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.
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 RSCALE(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 cggbal(3P)
