ctgevc(3P) Sun Performance Library ctgevc(3P)NAMEctgevc - compute some or all of the right and/or left generalized
eigenvectors of a pair of complex upper triangular matrices (A,B) that
was obtained from from the generalized Schur factorization of an origi‐
nal pair of complex nonsymmetric matrices. A and B are upper triangu‐
lar matrices and B must have real diagonal elements.
SYNOPSIS
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, complex *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, complex *vl, long ldvl,
complex *vr, long ldvr, long mm, long *m, long *info);
PURPOSEctgevc computes some or all of the right and/or left generalized eigen‐
vectors of a pair of complex upper triangular matrices (A,B) that was
obtained from from the generalized Schur factorization of an original
pair of complex nonsymmetric matrices (AO,BO). A and B are upper tri‐
angular matrices and B must have real diagonal elements.
The right generalized eigenvector x and the left generalized eigenvec‐
tor y of (A,B) corresponding to a generalized eigenvalue 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 generalized Schur factorization of an orig‐
inal 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 eigenvectors of A.
ARGUMENTS
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 back‐
transform 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 com‐
puted. 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 con‐
tain 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 contains: 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 otherwise.
VR (input/output)
On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must con‐
tain 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 otherwise.
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 illegal value.
6 Mar 2009 ctgevc(3P)
