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