SUBROUTINE SGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB, * SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, * BWORK, INFO) CHARACTER * 1 JOBVSL, JOBVSR, SORT INTEGER N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, INFO LOGICAL SELCTG LOGICAL BWORK(*) REAL A(LDA,*), B(LDB,*), ALPHAR(*), ALPHAI(*), BETA(*), VSL(LDVSL,*), VSR(LDVSR,*), WORK(*) SUBROUTINE SGGES_64( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, * LDB, SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, * LWORK, BWORK, INFO) CHARACTER * 1 JOBVSL, JOBVSR, SORT INTEGER*8 N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, INFO LOGICAL*8 SELCTG LOGICAL*8 BWORK(*) REAL A(LDA,*), B(LDB,*), ALPHAR(*), ALPHAI(*), BETA(*), VSL(LDVSL,*), VSR(LDVSR,*), WORK(*)
SUBROUTINE GGES( JOBVSL, JOBVSR, SORT, SELCTG, [N], A, [LDA], B, * [LDB], SDIM, ALPHAR, ALPHAI, BETA, VSL, [LDVSL], VSR, [LDVSR], * [WORK], [LWORK], [BWORK], [INFO]) CHARACTER(LEN=1) :: JOBVSL, JOBVSR, SORT INTEGER :: N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, INFO LOGICAL :: SELCTG LOGICAL, DIMENSION(:) :: BWORK REAL, DIMENSION(:) :: ALPHAR, ALPHAI, BETA, WORK REAL, DIMENSION(:,:) :: A, B, VSL, VSR SUBROUTINE GGES_64( JOBVSL, JOBVSR, SORT, SELCTG, [N], A, [LDA], B, * [LDB], SDIM, ALPHAR, ALPHAI, BETA, VSL, [LDVSL], VSR, [LDVSR], * [WORK], [LWORK], [BWORK], [INFO]) CHARACTER(LEN=1) :: JOBVSL, JOBVSR, SORT INTEGER(8) :: N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, INFO LOGICAL(8) :: SELCTG LOGICAL(8), DIMENSION(:) :: BWORK REAL, DIMENSION(:) :: ALPHAR, ALPHAI, BETA, WORK REAL, DIMENSION(:,:) :: A, B, VSL, VSR
void sgges(char jobvsl, char jobvsr, char sort, logical(*selctg)(float,float,float), int n, float *a, int lda, float *b, int ldb, int *sdim, float *alphar, float *alphai, float *beta, float *vsl, int ldvsl, float *vsr, int ldvsr, int *info);
void sgges_64(char jobvsl, char jobvsr, char sort, logical(*selctg)(float,float,float), long n, float *a, long lda, float *b, long ldb, long *sdim, float *alphar, float *alphai, float *beta, float *vsl, long ldvsl, float *vsr, long ldvsr, long *info);
(A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T )
Optionally, it also orders the eigenvalues so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix S and the upper triangular matrix T.The leading columns of VSL and VSR then form an orthonormal basis for the corresponding left and right eigenspaces (deflating subspaces).
(If only the generalized eigenvalues are needed, use the driver SGGEV instead, which is faster.)
A generalized eigenvalue for a pair of matrices (A,B) is a scalar w or a ratio alpha/beta = w, such that A - w*B is singular. It is usually represented as the pair (alpha,beta), as there is a reasonable interpretation for beta=0 or both being zero.
A pair of matrices (S,T) is in generalized real Schur form if T is upper triangular with non-negative diagonal and S is block upper triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond to real generalized eigenvalues, while 2-by-2 blocks of S will be ``standardized'' by making the corresponding elements of T have the form:
[ a 0 ] [ 0 b ]
and the pair of corresponding 2-by-2 blocks in S and T will have a complex conjugate pair of generalized eigenvalues.
Note that in the ill-conditioned case, a selected complex eigenvalue may no longer satisfy SELCTG(ALPHAR(j),ALPHAI(j), BETA(j)) = .TRUE. after ordering. INFO is to be set to N+2 in this case.
Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) may easily over- or underflow, and BETA(j) may even be zero. Thus, the user should avoid naively computing the ratio. However, ALPHAR and ALPHAI will be always less than and usually comparable with norm(A) in magnitude, and BETA always less than and usually comparable with norm(B).
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.