Contents
ctgevc - compute some or all of the right and/or left gen-
eralized eigenvectors of a pair of complex upper triangular
matrices (A,B)
SUBROUTINE CTGEVC(SIDE, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, LDVL,
VR, LDVR, MM, M, WORK, RWORK, INFO)
CHARACTER * 1 SIDE, HOWMNY
COMPLEX A(LDA,*), B(LDB,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
INTEGER N, LDA, LDB, LDVL, LDVR, MM, M, INFO
LOGICAL SELECT(*)
REAL RWORK(*)
SUBROUTINE CTGEVC_64(SIDE, HOWMNY, SELECT, N, A, LDA, B, LDB, VL,
LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO)
CHARACTER * 1 SIDE, HOWMNY
COMPLEX A(LDA,*), B(LDB,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
INTEGER*8 N, LDA, LDB, LDVL, LDVR, MM, M, INFO
LOGICAL*8 SELECT(*)
REAL RWORK(*)
F95 INTERFACE
SUBROUTINE TGEVC(SIDE, HOWMNY, SELECT, [N], A, [LDA], B, [LDB], VL,
[LDVL], VR, [LDVR], MM, M, [WORK], [RWORK], [INFO])
CHARACTER(LEN=1) :: SIDE, HOWMNY
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, B, VL, VR
INTEGER :: N, LDA, LDB, LDVL, LDVR, MM, M, INFO
LOGICAL, DIMENSION(:) :: SELECT
REAL, DIMENSION(:) :: RWORK
SUBROUTINE TGEVC_64(SIDE, HOWMNY, SELECT, [N], A, [LDA], B, [LDB],
VL, [LDVL], VR, [LDVR], MM, M, [WORK], [RWORK], [INFO])
CHARACTER(LEN=1) :: SIDE, HOWMNY
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, B, VL, VR
INTEGER(8) :: N, LDA, LDB, LDVL, LDVR, MM, M, INFO
LOGICAL(8), DIMENSION(:) :: SELECT
REAL, DIMENSION(:) :: RWORK
C INTERFACE
#include <sunperf.h>
void ctgevc(char side, char howmny, int *select, int n, com-
plex *a, int lda, complex *b, int ldb, complex
*vl, int ldvl, complex *vr, int ldvr, int mm, int
*m, int *info);
void ctgevc_64(char side, char howmny, long *select, long n,
complex *a, long lda, complex *b, long ldb, com-
plex *vl, long ldvl, complex *vr, long ldvr, long
mm, long *m, long *info);
ctgevc computes some or all of the right and/or left gen-
eralized eigenvectors of a pair of complex upper triangular
matrices (A,B).
The right generalized eigenvector x and the left generalized
eigenvector y of (A,B) corresponding to a generalized eigen-
value w are defined by:
(A - wB) * x = 0 and y**H * (A - wB) = 0
where y**H denotes the conjugate tranpose of y.
If an eigenvalue w is determined by zero diagonal elements
of both A and B, a unit vector is returned as the
corresponding eigenvector.
If all eigenvectors are requested, the routine may either
return the matrices X and/or Y of right or left eigenvectors
of (A,B), or the products Z*X and/or Q*Y, where Z and Q are
input unitary matrices. If (A,B) was obtained from the gen-
eralized Schur factorization of an original pair of matrices
(A0,B0) = (Q*A*Z**H,Q*B*Z**H),
then Z*X and Q*Y are the matrices of right or left eigenvec-
tors of A.
SIDE (input)
= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors.
HOWMNY (input)
= 'A': compute all right and/or left eigenvectors;
= 'B': compute all right and/or left eigenvectors,
and backtransform them using the input matrices
supplied in VR and/or VL; = 'S': compute selected
right and/or left eigenvectors, specified by the
logical array SELECT.
SELECT (input)
If HOWMNY='S', SELECT specifies the eigenvectors
to be computed. If HOWMNY='A' or 'B', SELECT is
not referenced. To select the eigenvector
corresponding to the j-th eigenvalue, SELECT(j)
must be set to .TRUE..
N (input) The order of the matrices A and B. N >= 0.
A (input) The upper triangular matrix A.
LDA (input)
The leading dimension of array A. LDA >=
max(1,N).
B (input) The upper triangular matrix B. B must have real
diagonal elements.
LDB (input)
The leading dimension of array B. LDB >=
max(1,N).
VL (input/output)
On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B',
VL must contain an N-by-N matrix Q (usually the
unitary matrix Q of left Schur vectors returned by
CHGEQZ). On exit, if SIDE = 'L' or 'B', VL con-
tains: if HOWMNY = 'A', the matrix Y of left
eigenvectors of (A,B); if HOWMNY = 'B', the matrix
Q*Y; if HOWMNY = 'S', the left eigenvectors of
(A,B) specified by SELECT, stored consecutively in
the columns of VL, in the same order as their
eigenvalues. If SIDE = 'R', VL is not referenced.
LDVL (input)
The leading dimension of array VL. LDVL >=
max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 other-
wise.
VR (input/output)
On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B',
VR must contain an N-by-N matrix Q (usually the
unitary matrix Z of right Schur vectors returned
by CHGEQZ). On exit, if SIDE = 'R' or 'B', VR
contains: if HOWMNY = 'A', the matrix X of right
eigenvectors of (A,B); if HOWMNY = 'B', the matrix
Z*X; if HOWMNY = 'S', the right eigenvectors of
(A,B) specified by SELECT, stored consecutively in
the columns of VR, in the same order as their
eigenvalues. If SIDE = 'L', VR is not referenced.
LDVR (input)
The leading dimension of the array VR. LDVR >=
max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 other-
wise.
MM (input)
The number of columns in the arrays VL and/or VR.
MM >= M.
M (output)
The number of columns in the arrays VL and/or VR
actually used to store the eigenvectors. If
HOWMNY = 'A' or 'B', M is set to N. Each selected
eigenvector occupies one column.
WORK (workspace)
dimension(2*N)
RWORK (workspace)
dimension(2*N)
INFO (output)
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille-
gal value.