cgegs - routine is deprecated and has been replaced by routine CGGES
SUBROUTINE CGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, * VSL, LDVSL, VSR, LDVSR, WORK, LDWORK, WORK2, INFO) CHARACTER * 1 JOBVSL, JOBVSR COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), VSL(LDVSL,*), VSR(LDVSR,*), WORK(*) INTEGER N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO REAL WORK2(*)
SUBROUTINE CGEGS_64( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, * VSL, LDVSL, VSR, LDVSR, WORK, LDWORK, WORK2, INFO) CHARACTER * 1 JOBVSL, JOBVSR COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), VSL(LDVSL,*), VSR(LDVSR,*), WORK(*) INTEGER*8 N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO REAL WORK2(*)
SUBROUTINE GEGS( JOBVSL, JOBVSR, [N], A, [LDA], B, [LDB], ALPHA, * BETA, VSL, [LDVSL], VSR, [LDVSR], [WORK], [LDWORK], [WORK2], * [INFO]) CHARACTER(LEN=1) :: JOBVSL, JOBVSR COMPLEX, DIMENSION(:) :: ALPHA, BETA, WORK COMPLEX, DIMENSION(:,:) :: A, B, VSL, VSR INTEGER :: N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO REAL, DIMENSION(:) :: WORK2
SUBROUTINE GEGS_64( JOBVSL, JOBVSR, [N], A, [LDA], B, [LDB], ALPHA, * BETA, VSL, [LDVSL], VSR, [LDVSR], [WORK], [LDWORK], [WORK2], * [INFO]) CHARACTER(LEN=1) :: JOBVSL, JOBVSR COMPLEX, DIMENSION(:) :: ALPHA, BETA, WORK COMPLEX, DIMENSION(:,:) :: A, B, VSL, VSR INTEGER(8) :: N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO REAL, DIMENSION(:) :: WORK2
#include <sunperf.h>
void cgegs(char jobvsl, char jobvsr, int n, complex *a, int lda, complex *b, int ldb, complex *alpha, complex *beta, complex *vsl, int ldvsl, complex *vsr, int ldvsr, int *info);
void cgegs_64(char jobvsl, char jobvsr, long n, complex *a, long lda, complex *b, long ldb, complex *alpha, complex *beta, complex *vsl, long ldvsl, complex *vsr, long ldvsr, long *info);
cgegs routine is deprecated and has been replaced by routine CGGES.
CGEGS computes for a pair of N-by-N complex nonsymmetric matrices A, B: the generalized eigenvalues (alpha, beta), the complex Schur form (A, B), and optionally left and/or right Schur vectors (VSL and VSR).
(If only the generalized eigenvalues are needed, use the driver CGEGV instead.)
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)
The (generalized) Schur form of a pair of matrices is the result of multiplying both matrices on the left by one unitary matrix and both on the right by another unitary matrix, these two unitary matrices being chosen so as to bring the pair of matrices into upper triangular form with the diagonal elements of B being non-negative real numbers (this is also called complex Schur form.)
The left and right Schur vectors are the columns of VSL and VSR, respectively, where VSL and VSR are the unitary matrices
which reduce A and B to Schur form:
Schur form of (A,B) = ( (VSL)**H A (VSR), (VSL)**H B (VSR) )
= 'N': do not compute the left Schur vectors;
= 'V': compute the left Schur vectors.
= 'N': do not compute the right Schur vectors;
= 'V': compute the right Schur vectors.
BETA(j)
will be non-negative real.
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).
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.
dimension(3*N)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
=1,...,N: The QZ iteration failed. (A,B) are not in Schur form, but ALPHA(j) and BETA(j) should be correct for j =INFO+1,...,N. > N: errors that usually indicate LAPACK problems:
=N+1: error return from CGGBAL
=N+2: error return from CGEQRF
=N+3: error return from CUNMQR
=N+4: error return from CUNGQR
=N+5: error return from CGGHRD
=N+6: error return from CHGEQZ (other than failed iteration) =N+7: error return from CGGBAK (computing VSL)
=N+8: error return from CGGBAK (computing VSR)
=N+9: error return from CLASCL (various places)