ztrevc - compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
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);
Oracle Solaris Studio Performance Library ztrevc(3P)
NAME
ztrevc - 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);
PURPOSE
ztrevc 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|.
7 Nov 2015 ztrevc(3P)