ztrevc(3P) Sun Performance Library ztrevc(3P)NAMEztrevc - compute some or all of the right and/or left eigenvectors of a
complex upper triangular matrix T
SYNOPSIS
SUBROUTINE ZTREVC(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
LDVR, MM, M, WORK, RWORK, INFO)
CHARACTER * 1 SIDE, HOWMNY
DOUBLE COMPLEX T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
INTEGER N, LDT, LDVL, LDVR, MM, M, INFO
LOGICAL SELECT(*)
DOUBLE PRECISION RWORK(*)
SUBROUTINE ZTREVC_64(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
LDVR, MM, M, WORK, RWORK, INFO)
CHARACTER * 1 SIDE, HOWMNY
DOUBLE COMPLEX T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
INTEGER*8 N, LDT, LDVL, LDVR, MM, M, INFO
LOGICAL*8 SELECT(*)
DOUBLE PRECISION 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(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: T, VL, VR
INTEGER :: N, LDT, LDVL, LDVR, MM, M, INFO
LOGICAL, DIMENSION(:) :: SELECT
REAL(8), 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(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: T, VL, VR
INTEGER(8) :: N, LDT, LDVL, LDVR, MM, M, INFO
LOGICAL(8), DIMENSION(:) :: SELECT
REAL(8), DIMENSION(:) :: RWORK
C INTERFACE
#include <sunperf.h>
void ztrevc(char side, char howmny, int *select, int n, doublecomplex
*t, int ldt, doublecomplex *vl, int ldvl, doublecomplex *vr,
int ldvr, int mm, int *m, int *info);
void ztrevc_64(char side, char howmny, long *select, long n, doublecom‐
plex *t, long ldt, doublecomplex *vl, long ldvl, doublecom‐
plex *vr, long ldvr, long mm, long *m, long *info);
PURPOSEztrevc computes some or all of the right and/or left eigenvectors 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.
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/output)
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 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 con‐
tain 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 contains: 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 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 Q of
Schur vectors returned by CHSEQR). On exit, if SIDE = 'R' or
'B', VR contains: 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
eigenvectors of T 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(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
FURTHER DETAILS
The algorithm used in this program is basically backward (forward) sub‐
stitution, with scaling to make the the code robust against possible
overflow.
Each eigenvector is normalized so that the element of largest magnitude
has magnitude 1; here the magnitude of a complex number (x,y) is taken
to be |x| + |y|.
6 Mar 2009 ztrevc(3P)
