SUBROUTINE DGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, * BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO) CHARACTER * 1 JOBVL, JOBVR INTEGER N, LDA, LDB, LDVL, LDVR, LWORK, INFO DOUBLE PRECISION A(LDA,*), B(LDB,*), ALPHAR(*), ALPHAI(*), BETA(*), VL(LDVL,*), VR(LDVR,*), WORK(*) SUBROUTINE DGGEV_64( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, * ALPHAI, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO) CHARACTER * 1 JOBVL, JOBVR INTEGER*8 N, LDA, LDB, LDVL, LDVR, LWORK, INFO DOUBLE PRECISION A(LDA,*), B(LDB,*), ALPHAR(*), ALPHAI(*), BETA(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
SUBROUTINE GGEV( JOBVL, JOBVR, [N], A, [LDA], B, [LDB], ALPHAR, * ALPHAI, BETA, VL, [LDVL], VR, [LDVR], [WORK], [LWORK], [INFO]) CHARACTER(LEN=1) :: JOBVL, JOBVR INTEGER :: N, LDA, LDB, LDVL, LDVR, LWORK, INFO REAL(8), DIMENSION(:) :: ALPHAR, ALPHAI, BETA, WORK REAL(8), DIMENSION(:,:) :: A, B, VL, VR SUBROUTINE GGEV_64( JOBVL, JOBVR, [N], A, [LDA], B, [LDB], ALPHAR, * ALPHAI, BETA, VL, [LDVL], VR, [LDVR], [WORK], [LWORK], [INFO]) CHARACTER(LEN=1) :: JOBVL, JOBVR INTEGER(8) :: N, LDA, LDB, LDVL, LDVR, LWORK, INFO REAL(8), DIMENSION(:) :: ALPHAR, ALPHAI, BETA, WORK REAL(8), DIMENSION(:,:) :: A, B, VL, VR
void dggev(char jobvl, char jobvr, int n, double *a, int lda, double *b, int ldb, double *alphar, double *alphai, double *beta, double *vl, int ldvl, double *vr, int ldvr, int *info);
void dggev_64(char jobvl, char jobvr, long n, double *a, long lda, double *b, long ldb, double *alphar, double *alphai, double *beta, double *vl, long ldvl, double *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 eigenvector v(j) corresponding to the eigenvalue lambda(j) of (A,B) satisfies
A * v(j) = lambda(j) * B * v(j).
The left eigenvector u(j) corresponding to the eigenvalue 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 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 alpha/beta. 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.