zggbal(3P) Sun Performance Library zggbal(3P)NAMEzggbal - balance a pair of general complex matrices (A,B)
SYNOPSIS
SUBROUTINE ZGGBAL(JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE,
WORK, INFO)
CHARACTER * 1 JOB
DOUBLE COMPLEX A(LDA,*), B(LDB,*)
INTEGER N, LDA, LDB, ILO, IHI, INFO
DOUBLE PRECISION LSCALE(*), RSCALE(*), WORK(*)
SUBROUTINE ZGGBAL_64(JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE,
RSCALE, WORK, INFO)
CHARACTER * 1 JOB
DOUBLE COMPLEX A(LDA,*), B(LDB,*)
INTEGER*8 N, LDA, LDB, ILO, IHI, INFO
DOUBLE PRECISION LSCALE(*), RSCALE(*), WORK(*)
F95 INTERFACE
SUBROUTINE GGBAL(JOB, [N], A, [LDA], B, [LDB], ILO, IHI, LSCALE,
RSCALE, [WORK], [INFO])
CHARACTER(LEN=1) :: JOB
COMPLEX(8), DIMENSION(:,:) :: A, B
INTEGER :: N, LDA, LDB, ILO, IHI, INFO
REAL(8), DIMENSION(:) :: LSCALE, RSCALE, WORK
SUBROUTINE GGBAL_64(JOB, [N], A, [LDA], B, [LDB], ILO, IHI, LSCALE,
RSCALE, [WORK], [INFO])
CHARACTER(LEN=1) :: JOB
COMPLEX(8), DIMENSION(:,:) :: A, B
INTEGER(8) :: N, LDA, LDB, ILO, IHI, INFO
REAL(8), DIMENSION(:) :: LSCALE, RSCALE, WORK
C INTERFACE
#include <sunperf.h>
void zggbal(char job, int n, doublecomplex *a, int lda, doublecomplex
*b, int ldb, int *ilo, int *ihi, double *lscale, double
*rscale, int *info);
void zggbal_64(char job, long n, doublecomplex *a, long lda, doublecom‐
plex *b, long ldb, long *ilo, long *ihi, double *lscale, dou‐
ble *rscale, long *info);
PURPOSEzggbal 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 zggbal(3P)
