SUBROUTINE ZGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, * VSL, LDVSL, VSR, LDVSR, WORK, LDWORK, WORK2, INFO) CHARACTER * 1 JOBVSL, JOBVSR DOUBLE COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), VSL(LDVSL,*), VSR(LDVSR,*), WORK(*) INTEGER N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO DOUBLE PRECISION WORK2(*) SUBROUTINE ZGEGS_64( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, * VSL, LDVSL, VSR, LDVSR, WORK, LDWORK, WORK2, INFO) CHARACTER * 1 JOBVSL, JOBVSR DOUBLE COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), VSL(LDVSL,*), VSR(LDVSR,*), WORK(*) INTEGER*8 N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO DOUBLE PRECISION 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(8), DIMENSION(:) :: ALPHA, BETA, WORK COMPLEX(8), DIMENSION(:,:) :: A, B, VSL, VSR INTEGER :: N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO REAL(8), 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(8), DIMENSION(:) :: ALPHA, BETA, WORK COMPLEX(8), DIMENSION(:,:) :: A, B, VSL, VSR INTEGER(8) :: N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO REAL(8), DIMENSION(:) :: WORK2
void zgegs(char jobvsl, char jobvsr, int n, doublecomplex *a, int lda, doublecomplex *b, int ldb, doublecomplex *alpha, doublecomplex *beta, doublecomplex *vsl, int ldvsl, doublecomplex *vsr, int ldvsr, int *info);
void zgegs_64(char jobvsl, char jobvsr, long n, doublecomplex *a, long lda, doublecomplex *b, long ldb, doublecomplex *alpha, doublecomplex *beta, doublecomplex *vsl, long ldvsl, doublecomplex *vsr, long ldvsr, long *info);
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) )
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 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.