!>
!> DTREVC computes some or all of the right and/or left eigenvectors of
!> a real upper quasi-triangular matrix T.
!> Matrices of this type are produced by the Schur factorization of
!> a real general matrix:  A = Q*T*Q**T, as computed by DHSEQR.
!>
!> The right eigenvector x and the left eigenvector y of T corresponding
!> to an eigenvalue w are defined by:
!>
!>    T*x = w*x,     (y**H)*T = w*(y**H)
!>
!> where y**H denotes the conjugate transpose of y.
!> The eigenvalues are not input to this routine, but are read directly
!> from the diagonal blocks of T.
!>
!> This routine returns the matrices X and/or Y of right and left
!> eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an
!> input matrix.  If Q is the orthogonal factor that reduces a matrix
!> A to Schur form T, then Q*X and Q*Y are the matrices of right and
!> left eigenvectors of A.
!> 

SIDE

!>          SIDE is CHARACTER*1
!>          = 'R':  compute right eigenvectors only;
!>          = 'L':  compute left eigenvectors only;
!>          = 'B':  compute both right and left eigenvectors.
!> 

HOWMNY

!>          HOWMNY is CHARACTER*1
!>          = 'A':  compute all right and/or left eigenvectors;
!>          = 'B':  compute all right and/or left eigenvectors,
!>                  backtransformed by the matrices in VR and/or VL;
!>          = 'S':  compute selected right and/or left eigenvectors,
!>                  as indicated by the logical array SELECT.
!> 

SELECT

!>          SELECT is LOGICAL array, dimension (N)
!>          If HOWMNY = 'S', SELECT specifies the eigenvectors to be
!>          computed.
!>          If w(j) is a real eigenvalue, the corresponding real
!>          eigenvector is computed if SELECT(j) is .TRUE..
!>          If w(j) and w(j+1) are the real and imaginary parts of a
!>          complex eigenvalue, the corresponding complex eigenvector is
!>          computed if either SELECT(j) or SELECT(j+1) is .TRUE., and
!>          on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to
!>          .FALSE..
!>          Not referenced if HOWMNY = 'A' or 'B'.
!> 

N

!>          N is INTEGER
!>          The order of the matrix T. N >= 0.
!> 

T

!>          T is DOUBLE PRECISION array, dimension (LDT,N)
!>          The upper quasi-triangular matrix T in Schur canonical form.
!> 

LDT

!>          LDT is INTEGER
!>          The leading dimension of the array T. LDT >= max(1,N).
!> 

VL

!>          VL is DOUBLE PRECISION 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 orthogonal matrix Q
!>          of Schur vectors returned by DHSEQR).
!>          On exit, if SIDE = 'L' or 'B', VL contains:
!>          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
!>                           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.
!>          Not referenced if SIDE = 'R'.
!> 

LDVL

!>          LDVL is INTEGER
!>          The leading dimension of the array VL.  LDVL >= 1, and if
!>          SIDE = 'L' or 'B', LDVL >= N.
!> 

VR

!>          VR is DOUBLE PRECISION 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 orthogonal matrix Q
!>          of Schur vectors returned by DHSEQR).
!>          On exit, if SIDE = 'R' or 'B', VR contains:
!>          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
!>                           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.
!>          Not referenced if SIDE = 'L'.
!> 

LDVR

!>          LDVR is INTEGER
!>          The leading dimension of the array VR.  LDVR >= 1, and if
!>          SIDE = 'R' or 'B', LDVR >= N.
!> 

MM

!>          MM is INTEGER
!>          The number of columns in the arrays VL and/or VR. MM >= M.
!> 

M

!>          M is 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 real eigenvector occupies one column and each
!>          selected complex eigenvector occupies two columns.
!> 

WORK

!>          WORK is DOUBLE PRECISION array, dimension (3*N)
!> 

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!>  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|.
!>