SUBROUTINE CGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL, * LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO) CHARACTER * 1 JOBVL, JOBVR COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), VL(LDVL,*), VR(LDVR,*), WORK(*) INTEGER N, LDA, LDB, LDVL, LDVR, LWORK, INFO REAL RWORK(*) SUBROUTINE CGGEV_64( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, * VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO) CHARACTER * 1 JOBVL, JOBVR COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), VL(LDVL,*), VR(LDVR,*), WORK(*) INTEGER*8 N, LDA, LDB, LDVL, LDVR, LWORK, INFO REAL RWORK(*)
SUBROUTINE GGEV( JOBVL, JOBVR, [N], A, [LDA], B, [LDB], ALPHA, BETA, * VL, [LDVL], VR, [LDVR], [WORK], [LWORK], [RWORK], [INFO]) CHARACTER(LEN=1) :: JOBVL, JOBVR COMPLEX, DIMENSION(:) :: ALPHA, BETA, WORK COMPLEX, DIMENSION(:,:) :: A, B, VL, VR INTEGER :: N, LDA, LDB, LDVL, LDVR, LWORK, INFO REAL, DIMENSION(:) :: RWORK SUBROUTINE GGEV_64( JOBVL, JOBVR, [N], A, [LDA], B, [LDB], ALPHA, * BETA, VL, [LDVL], VR, [LDVR], [WORK], [LWORK], [RWORK], [INFO]) CHARACTER(LEN=1) :: JOBVL, JOBVR COMPLEX, DIMENSION(:) :: ALPHA, BETA, WORK COMPLEX, DIMENSION(:,:) :: A, B, VL, VR INTEGER(8) :: N, LDA, LDB, LDVL, LDVR, LWORK, INFO REAL, DIMENSION(:) :: RWORK
void cggev(char jobvl, char jobvr, int n, complex *a, int lda, complex *b, int ldb, complex *alpha, complex *beta, complex *vl, int ldvl, complex *vr, int ldvr, int *info);
void cggev_64(char jobvl, char jobvr, long n, complex *a, long lda, complex *b, long ldb, complex *alpha, complex *beta, complex *vl, long ldvl, complex *vr, long ldvr, long *info);
A generalized eigenvalue for a pair of matrices (A,B) is a scalar lambda or a ratio alpha/beta = lambda, such that A - lambda*B is singular. It is usually represented as the pair (alpha,beta), as there is a reasonable interpretation for beta=0, and even for both being zero.
The right generalized eigenvector v(j) corresponding to the generalized eigenvalue lambda(j) of (A,B) satisfies
A * v(j) = lambda(j) * B * v(j).
The left generalized eigenvector u(j) corresponding to the generalized eigenvalues lambda(j) of (A,B) satisfies
u(j)**H * A = lambda(j) * u(j)**H * B
where u(j)**H is the conjugate-transpose of u(j).
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).
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.