Contents
ctrevc - compute some or all of the right and/or left eigen-
vectors of a complex upper triangular matrix T
SUBROUTINE CTREVC(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
LDVR, MM, M, WORK, RWORK, INFO)
CHARACTER * 1 SIDE, HOWMNY
COMPLEX T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
INTEGER N, LDT, LDVL, LDVR, MM, M, INFO
LOGICAL SELECT(*)
REAL RWORK(*)
SUBROUTINE CTREVC_64(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
LDVR, MM, M, WORK, RWORK, INFO)
CHARACTER * 1 SIDE, HOWMNY
COMPLEX T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
INTEGER*8 N, LDT, LDVL, LDVR, MM, M, INFO
LOGICAL*8 SELECT(*)
REAL RWORK(*)
F95 INTERFACE
SUBROUTINE TREVC(SIDE, HOWMNY, SELECT, [N], T, [LDT], VL, [LDVL], VR,
[LDVR], MM, M, [WORK], [RWORK], [INFO])
CHARACTER(LEN=1) :: SIDE, HOWMNY
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: T, VL, VR
INTEGER :: N, LDT, LDVL, LDVR, MM, M, INFO
LOGICAL, DIMENSION(:) :: SELECT
REAL, DIMENSION(:) :: RWORK
SUBROUTINE TREVC_64(SIDE, HOWMNY, SELECT, [N], T, [LDT], VL, [LDVL],
VR, [LDVR], MM, M, [WORK], [RWORK], [INFO])
CHARACTER(LEN=1) :: SIDE, HOWMNY
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: T, VL, VR
INTEGER(8) :: N, LDT, LDVL, LDVR, MM, M, INFO
LOGICAL(8), DIMENSION(:) :: SELECT
REAL, DIMENSION(:) :: RWORK
C INTERFACE
#include <sunperf.h>
void ctrevc(char side, char howmny, int *select, int n, com-
plex *t, int ldt, complex *vl, int ldvl, complex
*vr, int ldvr, int mm, int *m, int *info);
void ctrevc_64(char side, char howmny, long *select, long n,
complex *t, long ldt, complex *vl, long ldvl, com-
plex *vr, long ldvr, long mm, long *m, long
*info);
ctrevc computes some or all of the right and/or left eigen-
vectors of a complex upper triangular matrix T.
The right eigenvector x and the left eigenvector y of T
corresponding to an eigenvalue w are defined by:
T*x = w*x, y'*T = w*y'
where y' denotes the conjugate transpose of the vector y.
If all eigenvectors are requested, the routine may either
return the matrices X and/or Y of right or left eigenvectors
of T, or the products Q*X and/or Q*Y, where Q is an input
unitary
matrix. If T was obtained from the Schur factorization of an
original matrix A = Q*T*Q', then Q*X and Q*Y are the
matrices of right or left eigenvectors 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 eigenvec-
tors;
= 'B': compute all right and/or left eigenvec-
tors, 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/output)
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 matrix T. N >= 0.
T (input/output)
The upper triangular matrix T. T is modified, but
restored on exit.
LDT (input)
The leading dimension of the array T. LDT >=
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 Schur vectors returned by
CHSEQR). On exit, if SIDE = 'L' or 'B', VL con-
tains: if HOWMNY = 'A', the matrix Y of left
eigenvectors of T; VL is lower triangular. The i-
th column VL(i) of VL is the eigenvector
corresponding to T(i,i). if HOWMNY = 'B', the
matrix Q*Y; if HOWMNY = 'S', the left eigenvectors
of T 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 the 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 Q of Schur vectors returned by
CHSEQR). On exit, if SIDE = 'R' or 'B', VR con-
tains: if HOWMNY = 'A', the matrix X of right
eigenvectors of T; VR is upper triangular. The i-
th column VR(i) of VR is the eigenvector
corresponding to T(i,i). if HOWMNY = 'B', the
matrix Q*X; if HOWMNY = 'S', the right eigenvec-
tors of T specified by SELECT, stored consecu-
tively 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(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value
The algorithm used in this program is basically backward
(forward) substitution, with scaling to make the the code
robust against possible overflow.
Each eigenvector is normalized so that the element of larg-
est magnitude has magnitude 1; here the magnitude of a com-
plex number (x,y) is taken to be |x| + |y|.