dgegv - routine is deprecated and has been replaced by routine SGGEV
SUBROUTINE DGEGV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, * BETA, VL, LDVL, VR, LDVR, WORK, LDWORK, INFO) CHARACTER * 1 JOBVL, JOBVR INTEGER N, LDA, LDB, LDVL, LDVR, LDWORK, INFO DOUBLE PRECISION A(LDA,*), B(LDB,*), ALPHAR(*), ALPHAI(*), BETA(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
SUBROUTINE DGEGV_64( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, * ALPHAI, BETA, VL, LDVL, VR, LDVR, WORK, LDWORK, INFO) CHARACTER * 1 JOBVL, JOBVR INTEGER*8 N, LDA, LDB, LDVL, LDVR, LDWORK, INFO DOUBLE PRECISION A(LDA,*), B(LDB,*), ALPHAR(*), ALPHAI(*), BETA(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
SUBROUTINE GEGV( JOBVL, JOBVR, [N], A, [LDA], B, [LDB], ALPHAR, * ALPHAI, BETA, VL, [LDVL], VR, [LDVR], [WORK], [LDWORK], [INFO]) CHARACTER(LEN=1) :: JOBVL, JOBVR INTEGER :: N, LDA, LDB, LDVL, LDVR, LDWORK, INFO REAL(8), DIMENSION(:) :: ALPHAR, ALPHAI, BETA, WORK REAL(8), DIMENSION(:,:) :: A, B, VL, VR
SUBROUTINE GEGV_64( JOBVL, JOBVR, [N], A, [LDA], B, [LDB], ALPHAR, * ALPHAI, BETA, VL, [LDVL], VR, [LDVR], [WORK], [LDWORK], [INFO]) CHARACTER(LEN=1) :: JOBVL, JOBVR INTEGER(8) :: N, LDA, LDB, LDVL, LDVR, LDWORK, INFO REAL(8), DIMENSION(:) :: ALPHAR, ALPHAI, BETA, WORK REAL(8), DIMENSION(:,:) :: A, B, VL, VR
#include <sunperf.h>
void dgegv(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 dgegv_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);
dgegv routine is deprecated and has been replaced by routine SGGEV.
SGEGV computes for a pair of n-by-n real nonsymmetric matrices A and B, the generalized eigenvalues (alphar +/- alphai*i, beta), and optionally, the left and/or right generalized eigenvectors (VL and VR).
A generalized eigenvalue for a pair of matrices (A,B) is, roughly speaking, 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, and even for both being zero. A good beginning reference is the book, ``Matrix Computations'', by G. Golub & C. van Loan (Johns Hopkins U. Press)
A right generalized eigenvector corresponding to a generalized eigenvalue w for a pair of matrices (A,B) is a vector r such that (A - w B) r = 0 . A left generalized eigenvector is a vector l such that l**H * (A - w B) = 0, where l**H is the
conjugate-transpose of l.
Note: this routine performs ``full balancing'' on A and B -- see ``Further Details'', below.
= 'N': do not compute the left generalized eigenvectors;
= 'V': compute the left generalized eigenvectors.
= 'N': do not compute the right generalized eigenvectors;
= 'V': compute the right generalized eigenvectors.
ALPHAI(j) is zero, then
the j-th eigenvalue is real; if positive, then the j-th and
(j+1)-st eigenvalues are a complex conjugate pair, with
ALPHAI(j+1) negative.
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).
WORK(1) returns the optimal LDWORK.
If LDWORK = -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 LDWORK is issued by XERBLA.
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
= 1,...,N: The QZ iteration failed. No eigenvectors have been calculated, but ALPHAR(j), ALPHAI(j), and BETA(j) should be correct for j =INFO+1,...,N. > N: errors that usually indicate LAPACK problems:
=N+1: error return from SGGBAL
=N+2: error return from SGEQRF
=N+3: error return from SORMQR
=N+4: error return from SORGQR
=N+5: error return from SGGHRD
=N+6: error return from SHGEQZ (other than failed iteration) =N+7: error return from STGEVC
=N+8: error return from SGGBAK (computing VL)
=N+9: error return from SGGBAK (computing VR)
=N+10: error return from SLASCL (various calls)
Balancing
---------
This driver calls SGGBAL to both permute and scale rows and columns
of A and B. The permutations PL and PR are chosen so that PL*A*PR
and PL*B*R will be upper triangular except for the diagonal blocks
A(i:j,i:j) and B(i:j,i:j), with i and j as close together as
possible. The diagonal scaling matrices DL and DR are chosen so
that the pair DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to
one (except for the elements that start out zero.)
After the eigenvalues and eigenvectors of the balanced matrices have been computed, SGGBAK transforms the eigenvectors back to what they would have been (in perfect arithmetic) if they had not been balanced.
Contents of A and B on Exit
-------- -- - --- - -- ----
If any eigenvectors are computed (either JOBVL ='V' or JOBVR ='V' or both), then on exit the arrays A and B will contain the real Schur form[*] of the ``balanced'' versions of A and B. If no eigenvectors are computed, then only the diagonal blocks will be correct.
[*] See SHGEQZ, SGEGS, or read the book ``Matrix Computations'', by Golub & van Loan, pub. by Johns Hopkins U. Press.