Contents
strevc - compute some or all of the right and/or left eigen-
vectors 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(*)
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, 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
C INTERFACE
#include <sunperf.h>
void strevc(char side, char howmny, int *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, long *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 eigen-
vectors 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 diag-
onal 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 com-
plex 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.
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 real eigenvector
corresponding to a real eigenvalue w(j), 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..
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 contain 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 con-
tains: 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 eigen-
value, 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 correspond-
ing 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 contain 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 con-
tains: 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 eigen-
value, 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 correspond-
ing 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 eigen-
vector corresponding to a complex eigenvalue is
stored in two consecutive columns, the first hold-
ing 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 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
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
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|.