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.TH CTREVC l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
CTREVC - compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
.SH SYNOPSIS
.TP 19
SUBROUTINE CTREVC(
SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
LDVR, MM, M, WORK, RWORK, INFO )
.TP 19
.ti +4
CHARACTER
HOWMNY, SIDE
.TP 19
.ti +4
INTEGER
INFO, LDT, LDVL, LDVR, M, MM, N
.TP 19
.ti +4
LOGICAL
SELECT( * )
.TP 19
.ti +4
REAL
RWORK( * )
.TP 19
.ti +4
COMPLEX
T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ),
WORK( * )
.SH PURPOSE
CTREVC 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:
.br
T*x = w*x, y'*T = w*y'
.br
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
.br
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.
.br
.SH ARGUMENTS
.TP 8
SIDE (input) CHARACTER*1
= 'R': compute right eigenvectors only;
.br
= 'L': compute left eigenvectors only;
.br
= 'B': compute both right and left eigenvectors.
.TP 8
HOWMNY (input) CHARACTER*1
.br
= 'A': compute all right and/or left eigenvectors;
.br
= '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.
.TP 8
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 j-th
eigenvalue, SELECT(j) must be set to .TRUE..
.TP 8
N (input) INTEGER
The order of the matrix T. N >= 0.
.TP 8
T (input/output) COMPLEX array, dimension (LDT,N)
The upper triangular matrix T. T is modified, but restored
on exit.
.TP 8
LDT (input) INTEGER
The leading dimension of the array T. LDT >= max(1,N).
.TP 8
VL (input/output) COMPLEX array, dimension (LDVL,MM)
On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must
contain 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.
.TP 8
LDVL (input) INTEGER
The leading dimension of the array VL. LDVL >= max(1,N) if
SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
.TP 8
VR (input/output) COMPLEX array, dimension (LDVR,MM)
On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
contain 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.
.TP 8
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= max(1,N) if
SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
.TP 8
MM (input) INTEGER
The number of columns in the arrays VL and/or VR. MM >= M.
.TP 8
M (output) INTEGER
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.
.TP 8
WORK (workspace) COMPLEX array, dimension (2*N)
.TP 8
RWORK (workspace) REAL array, dimension (N)
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value
.SH FURTHER DETAILS
The algorithm used in this program is basically backward (forward)
substitution, with scaling to make the the code robust against
possible overflow.
.br
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|.
.br
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