Contents
zgegs - routine is deprecated and has been replaced by rou-
tine CGGES
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(*)
F95 INTERFACE
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
C INTERFACE
#include <sunperf.h>
void zgegs(char jobvsl, char jobvsr, int n, doublecomplex
*a, int lda, doublecomplex *b, int ldb, doublecom-
plex *alpha, doublecomplex *beta, doublecomplex
*vsl, int ldvsl, doublecomplex *vsr, int ldvsr,
int *info);
void zgegs_64(char jobvsl, char jobvsr, long n, doublecom-
plex *a, long lda, doublecomplex *b, long ldb,
doublecomplex *alpha, doublecomplex *beta, doub-
lecomplex *vsl, long ldvsl, doublecomplex *vsr,
long ldvsr, long *info);
zgegs routine is deprecated and has been replaced by routine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 interpre-
tation 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 uni-
tary 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 diago-
nal 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) )
JOBVSL (input)
= 'N': do not compute the left Schur vectors;
= 'V': compute the left Schur vectors.
JOBVSR (input)
= 'N': do not compute the right Schur vectors;
= 'V': compute the right Schur vectors.
N (input) The order of the matrices A, B, VSL, and VSR. N
>= 0.
A (input/output)
On entry, the first of the pair of matrices whose
generalized eigenvalues and (optionally) Schur
vectors are to be computed. On exit, the general-
ized Schur form of A.
LDA (input)
The leading dimension of A. LDA >= max(1,N).
B (input/output)
On entry, the second of the pair of matrices whose
generalized eigenvalues and (optionally) Schur
vectors are to be computed. On exit, the general-
ized Schur form of B.
LDB (input)
The leading dimension of B. LDB >= max(1,N).
ALPHA (output)
On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the
generalized eigenvalues. ALPHA(j), j=1,...,N and
BETA(j), j=1,...,N are the diagonals of the com-
plex Schur form (A,B) output by CGEGS. The
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).
BETA (output)
See the description of ALPHA.
VSL (input)
If JOBVSL = 'V', VSL will contain the left Schur
vectors. (See "Purpose", above.) Not referenced
if JOBVSL = 'N'.
LDVSL (input)
The leading dimension of the matrix VSL. LDVSL >=
1, and if JOBVSL = 'V', LDVSL >= N.
VSR (input)
If JOBVSR = 'V', VSR will contain the right Schur
vectors. (See "Purpose", above.) Not referenced
if JOBVSR = 'N'.
LDVSR (input)
The leading dimension of the matrix VSR. LDVSR >=
1, and if JOBVSR = 'V', LDVSR >= N.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LDWORK.
LDWORK (input)
The dimension of the array WORK. LDWORK >=
max(1,2*N). For good performance, LDWORK must
generally be larger. To compute the optimal value
of LDWORK, call ILAENV to get blocksizes (for
CGEQRF, CUNMQR, and CUNGQR.) Then compute: NB as
the MAX of the blocksizes for CGEQRF, CUNMQR, and
CUNGQR; the optimal LDWORK is N*(NB+1).
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.
WORK2 (workspace)
dimension(3*N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal 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 (comput-
ing VSL)
=N+8: error return from CGGBAK (computing VSR)
=N+9: error return from CLASCL (various places)