dtrevc - compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T
SUBROUTINE DTREVC(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, INFO) CHARACTER*1 SIDE, HOWMNY INTEGER N, LDT, LDVL, LDVR, MM, M, INFO LOGICAL SELECT(*) DOUBLE PRECISION T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*) SUBROUTINE DTREVC_64(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, INFO) CHARACTER*1 SIDE, HOWMNY INTEGER*8 N, LDT, LDVL, LDVR, MM, M, INFO LOGICAL*8 SELECT(*) DOUBLE PRECISION T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*) F95 INTERFACE SUBROUTINE TREVC(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, INFO) CHARACTER(LEN=1) :: SIDE, HOWMNY INTEGER :: N, LDT, LDVL, LDVR, MM, M, INFO LOGICAL, DIMENSION(:) :: SELECT REAL(8), DIMENSION(:) :: WORK REAL(8), DIMENSION(:,:) :: T, VL, VR SUBROUTINE TREVC_64(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, INFO) CHARACTER(LEN=1) :: SIDE, HOWMNY INTEGER(8) :: N, LDT, LDVL, LDVR, MM, M, INFO LOGICAL(8), DIMENSION(:) :: SELECT REAL(8), DIMENSION(:) :: WORK REAL(8), DIMENSION(:,:) :: T, VL, VR C INTERFACE #include <sunperf.h> void dtrevc(char side, char howmny, int *select, int n, double *t, int ldt, double *vl, int ldvl, double *vr, int ldvr, int mm, int *m, int *info); void dtrevc_64(char side, char howmny, long *select, long n, double *t, long ldt, double *vl, long ldvl, double *vr, long ldvr, long mm, long *m, long *info);
Oracle Solaris Studio Performance Library dtrevc(3P)
NAME
dtrevc - compute some or all of the right and/or left eigenvectors of a
real upper quasi-triangular matrix T
SYNOPSIS
SUBROUTINE DTREVC(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
LDVR, MM, M, WORK, INFO)
CHARACTER*1 SIDE, HOWMNY
INTEGER N, LDT, LDVL, LDVR, MM, M, INFO
LOGICAL SELECT(*)
DOUBLE PRECISION T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
SUBROUTINE DTREVC_64(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
LDVR, MM, M, WORK, INFO)
CHARACTER*1 SIDE, HOWMNY
INTEGER*8 N, LDT, LDVL, LDVR, MM, M, INFO
LOGICAL*8 SELECT(*)
DOUBLE PRECISION T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
F95 INTERFACE
SUBROUTINE TREVC(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
LDVR, MM, M, WORK, INFO)
CHARACTER(LEN=1) :: SIDE, HOWMNY
INTEGER :: N, LDT, LDVL, LDVR, MM, M, INFO
LOGICAL, DIMENSION(:) :: SELECT
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: T, VL, VR
SUBROUTINE TREVC_64(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL,
VR, LDVR, MM, M, WORK, INFO)
CHARACTER(LEN=1) :: SIDE, HOWMNY
INTEGER(8) :: N, LDT, LDVL, LDVR, MM, M, INFO
LOGICAL(8), DIMENSION(:) :: SELECT
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: T, VL, VR
C INTERFACE
#include <sunperf.h>
void dtrevc(char side, char howmny, int *select, int n, double *t, int
ldt, double *vl, int ldvl, double *vr, int ldvr, int mm, int
*m, int *info);
void dtrevc_64(char side, char howmny, long *select, long n, double *t,
long ldt, double *vl, long ldvl, double *vr, long ldvr, long
mm, long *m, long *info);
PURPOSE
dtrevc computes some or all of the right and/or left eigenvectors of a
real upper quasi-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 orthogonal
matrix. If T was obtained from the real-Schur factorization of an orig-
inal matrix A = Q*T*Q', then Q*X and Q*Y are the matrices of right or
left eigenvectors of A.
T must be in Schur canonical form (as returned by SHSEQR), that is,
block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
2-by-2 diagonal block has its diagonal elements equal and its off-diag-
onal elements of opposite sign. Corresponding to each 2-by-2 diagonal
block is a complex conjugate pair of eigenvalues and eigenvectors; only
one eigenvector of the pair is computed, namely the one corresponding
to the eigenvalue with positive imaginary part.
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 real eigenvector corresponding to a real eigenval-
ue w(j), SELECT(j) must be set to .TRUE.. To select the com-
plex eigenvector corresponding to a complex conjugate pair
w(j) and w(j+1), either SELECT(j) or SELECT(j+1) must be set
to .TRUE.; then on exit SELECT(j) is .TRUE. and SELECT(j+1)
is .FALSE..
N (input) The order of the matrix T. N >= 0.
T (input/output)
The upper quasi-triangular matrix T in Schur canonical form.
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 orthogonal matrix Q of
Schur vectors returned by SHSEQR). On exit, if SIDE = 'L' or
'B', VL contains: if HOWMNY = 'A', the matrix Y of left
eigenvectors of T; VL has the same quasi-lower triangular
form as T'. If T(i,i) is a real eigenvalue, then the i-th
column VL(i) of VL is its corresponding eigenvector. If
T(i:i+1,i:i+1) is a 2-by-2 block whose eigenvalues are com-
plex-conjugate eigenvalues of T, then VL(i)+sqrt(-1)*VL(i+1)
is the complex eigenvector corresponding to the eigenvalue
with positive real part. 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. A complex eigenvector corresponding to
a complex eigenvalue is stored in two consecutive columns,
the first holding the real part, and the second the imaginary
part. 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 orthogonal matrix Q of
Schur vectors returned by SHSEQR). On exit, if SIDE = 'R' or
'B', VR contains: if HOWMNY = 'A', the matrix X of right
eigenvectors of T; VR has the same quasi-upper triangular
form as T. If T(i,i) is a real eigenvalue, then the i-th col-
umn VR(i) of VR is its corresponding eigenvector. If
T(i:i+1,i:i+1) is a 2-by-2 block whose eigenvalues are com-
plex-conjugate eigenvalues of T, then VR(i)+sqrt(-1)*VR(i+1)
is the complex eigenvector corresponding to the eigenvalue
with positive real part. 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. A complex eigenvector cor-
responding to a complex eigenvalue is stored in two consecu-
tive columns, the first holding the real part and the second
the imaginary part. 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 real eigenvector occupies one column
and each selected complex eigenvector occupies two columns.
WORK (workspace)
dimension(3*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 dtrevc(3P)