SUBROUTINE CGGESX( JOBVSL, JOBVSR, SORT, SELCTG, SENSE, N, A, LDA, * B, LDB, SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, RCONDE, * RCONDV, WORK, LWORK, RWORK, IWORK, LIWORK, BWORK, INFO) CHARACTER * 1 JOBVSL, JOBVSR, SORT, SENSE COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), VSL(LDVSL,*), VSR(LDVSR,*), WORK(*) INTEGER N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, LIWORK, INFO INTEGER IWORK(*) LOGICAL SELCTG LOGICAL BWORK(*) REAL RCONDE(*), RCONDV(*), RWORK(*) SUBROUTINE CGGESX_64( JOBVSL, JOBVSR, SORT, SELCTG, SENSE, N, A, * LDA, B, LDB, SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, RCONDE, * RCONDV, WORK, LWORK, RWORK, IWORK, LIWORK, BWORK, INFO) CHARACTER * 1 JOBVSL, JOBVSR, SORT, SENSE COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), VSL(LDVSL,*), VSR(LDVSR,*), WORK(*) INTEGER*8 N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, LIWORK, INFO INTEGER*8 IWORK(*) LOGICAL*8 SELCTG LOGICAL*8 BWORK(*) REAL RCONDE(*), RCONDV(*), RWORK(*)
SUBROUTINE GGESX( JOBVSL, JOBVSR, SORT, SELCTG, SENSE, [N], A, [LDA], * B, [LDB], SDIM, ALPHA, BETA, VSL, [LDVSL], VSR, [LDVSR], RCONDE, * RCONDV, [WORK], [LWORK], [RWORK], [IWORK], [LIWORK], [BWORK], * [INFO]) CHARACTER(LEN=1) :: JOBVSL, JOBVSR, SORT, SENSE COMPLEX, DIMENSION(:) :: ALPHA, BETA, WORK COMPLEX, DIMENSION(:,:) :: A, B, VSL, VSR INTEGER :: N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, LIWORK, INFO INTEGER, DIMENSION(:) :: IWORK LOGICAL :: SELCTG LOGICAL, DIMENSION(:) :: BWORK REAL, DIMENSION(:) :: RCONDE, RCONDV, RWORK SUBROUTINE GGESX_64( JOBVSL, JOBVSR, SORT, SELCTG, SENSE, [N], A, * [LDA], B, [LDB], SDIM, ALPHA, BETA, VSL, [LDVSL], VSR, [LDVSR], * RCONDE, RCONDV, [WORK], [LWORK], [RWORK], [IWORK], [LIWORK], * [BWORK], [INFO]) CHARACTER(LEN=1) :: JOBVSL, JOBVSR, SORT, SENSE COMPLEX, DIMENSION(:) :: ALPHA, BETA, WORK COMPLEX, DIMENSION(:,:) :: A, B, VSL, VSR INTEGER(8) :: N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, LIWORK, INFO INTEGER(8), DIMENSION(:) :: IWORK LOGICAL(8) :: SELCTG LOGICAL(8), DIMENSION(:) :: BWORK REAL, DIMENSION(:) :: RCONDE, RCONDV, RWORK
void cggesx(char jobvsl, char jobvsr, char sort, logical(*selctg)(complex,complex), char sense, int n, complex *a, int lda, complex *b, int ldb, int *sdim, complex *alpha, complex *beta, complex *vsl, int ldvsl, complex *vsr, int ldvsr, float *rconde, float *rcondv, int *info);
void cggesx_64(char jobvsl, char jobvsr, char sort, logical(*selctg)(complex,complex), char sense, long n, complex *a, long lda, complex *b, long ldb, long *sdim, complex *alpha, complex *beta, complex *vsl, long ldvsl, complex *vsr, long ldvsr, float *rconde, float *rcondv, long *info);
where (VSR)**H is the conjugate-transpose of VSR.
Optionally, it also orders the eigenvalues so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper triangular matrix S and the upper triangular matrix T; computes a reciprocal condition number for the average of the selected eigenvalues (RCONDE); and computes a reciprocal condition number for the right and left deflating subspaces corresponding to the selected eigenvalues (RCONDV). The leading columns of VSL and VSR then form an orthonormal basis for the corresponding left and right eigenspaces (deflating subspaces).
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 for both being zero.
A pair of matrices (S,T) is in generalized complex Schur form if T is upper triangular with non-negative diagonal and S is upper triangular.
Note: the quotients ALPHA(j)/BETA(j) may easily over- or underflow, and BETA(j) may even be zero. Thus, the user should avoid naively computing the ratio alpha/beta. However, ALPHA will be always less than and usually comparable with norm(A) in magnitude, and BETA always less than and usually comparable with norm(B).