strevc - compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T
SUBROUTINE STREVC( 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(*) REAL T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
SUBROUTINE STREVC_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(*) REAL T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
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, DIMENSION(:) :: WORK REAL, 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, DIMENSION(:) :: WORK REAL, DIMENSION(:,:) :: T, VL, VR
#include <sunperf.h>
void strevc(char side, char howmny, logical *select, int n, float *t, int ldt, float *vl, int ldvl, float *vr, int ldvr, int mm, int *m, int *info);
void strevc_64(char side, char howmny, logical *select, long n, float *t, long ldt, float *vl, long ldvl, float *vr, long ldvr, long mm, long *m, long *info);
strevc 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 original 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-diagonal 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.
= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors.
= 'A': compute all right and/or left eigenvectors;
= 'B': compute all right and/or left eigenvectors, 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(j) must be set to .TRUE.. To select
the complex 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..
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
complex-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.
max(1,N) if
SIDE = 'L' or 'B'; LDVL > = 1 otherwise.
T(i,i) is a real eigenvalue, then
the i-th column 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
complex-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 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 = 'L', VR is not referenced.
max(1,N) if
SIDE = 'R' or 'B'; LDVR > = 1 otherwise.
dimension(3*N)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal 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 largest magnitude has magnitude 1; here the magnitude of a complex number (x,y) is taken to be |x| + |y|.