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NAME
     ctrevc - compute some or all of the right and/or left eigen-
     vectors of a complex upper triangular 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( * )



     #include <sunperf.h>

     void ctrevc(char side, char howmny, int *select, int n, com-
               plex  *t,  int ldt, complex *vl, int ldvl, complex
               *vr, int ldvr, int mm, int *m, int *info) ;

PURPOSE
     CTREVC computes some or all of the right and/or left  eigen-
     vectors 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:

                  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  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) 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..

     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 N-by-N matrix Q (usually the
               unitary matrix Q  of  Schur  vectors  returned  by
               CHSEQR).   On  exit, if SIDE = 'L' or 'B', VL con-
               tains:  if HOWMNY = 'A',  the  matrix  Y  of  left
               eigenvectors  of  T;  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  eigen-
               values.  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 other-
               wise.

     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 con-
               tains:  if HOWMNY = 'A', the  matrix  X  of  right
               eigenvectors  of  T;  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  eigen-
               values.  If SIDE = 'L', VR is not referenced.

     LDVR      (input) INTEGER
               The leading dimension of the array  VR.   LDVR  >=
               max(1,N)  if  SIDE  = 'R' or 'B'; LDVR >= 1 other-
               wise.

     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  eigenvectors.   If
               HOWMNY = 'A' or 'B', M is set to N.  Each selected
               eigenvector occupies 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 i-th argument had an ille-
               gal 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  larg-
     est  magnitude has magnitude 1; here the magnitude of a com-
     plex number (x,y) is taken to be |x| + |y|.

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