
CTREVC(l) ) CTREVC(l)
NAME
CTREVC  compute some or all of the right and/or left eigenvectors of a complex upper tri
angular matrix T
SYNOPSIS
SUBROUTINE CTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK,
RWORK, INFO )
CHARACTER HOWMNY, SIDE
INTEGER INFO, LDT, LDVL, LDVR, M, MM, N
LOGICAL SELECT( * )
REAL RWORK( * )
COMPLEX T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ), WORK( * )
PURPOSE
CTREVC computes some or all of the right and/or left eigenvectors of a complex upper tri
angular 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) CHARACTER*1
= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors.
HOWMNY (input) CHARACTER*1
= '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 (input) LOGICAL array, dimension (N)
If HOWMNY = 'S', SELECT specifies the eigenvectors to be computed. If HOWMNY =
'A' or 'B', SELECT is not referenced. To select the eigenvector corresponding to
the jth eigenvalue, SELECT(j) must be set to .TRUE..
N (input) INTEGER
The order of the matrix T. N >= 0.
T (input/output) COMPLEX array, dimension (LDT,N)
The upper triangular matrix T. T is modified, but restored on exit.
LDT (input) INTEGER
The leading dimension of the array T. LDT >= max(1,N).
VL (input/output) COMPLEX array, dimension (LDVL,MM)
On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must contain an NbyN 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 ith column VL(i) of VL is the eigenvector cor
responding 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) INTEGER
The leading dimension of the array VL. LDVL >= max(1,N) if SIDE = 'L' or 'B';
LDVL >= 1 otherwise.
VR (input/output) COMPLEX array, dimension (LDVR,MM)
On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must contain an NbyN 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 eigenvec
tors of T; VR is upper triangular. The ith 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 refer
enced.
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= max(1,N) if SIDE = 'R' or 'B';
LDVR >= 1 otherwise.
MM (input) INTEGER
The number of columns in the arrays VL and/or VR. MM >= M.
M (output) INTEGER
The number of columns in the arrays VL and/or VR actually used to store the eigen
vectors. If HOWMNY = 'A' or 'B', M is set to N. Each selected eigenvector occu
pies one column.
WORK (workspace) COMPLEX array, dimension (2*N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
FURTHER DETAILS
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.
LAPACK version 3.0 15 June 2000 CTREVC(l) 
