cggbal - balance a pair of general complex matrices (A,B)
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);
Oracle Solaris Studio Performance Library cggbal(3P)
NAME
cggbal - 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);
PURPOSE
cggbal 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.
7 Nov 2015 cggbal(3P)