NAME

       dtrevc.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dtrevc (SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, INFO)
           DTREVC

Function/Subroutine Documentation

   subroutine dtrevc (characterSIDE, characterHOWMNY, logical, dimension( * )SELECT, integerN,
       double precision, dimension( ldt, * )T, integerLDT, double precision, dimension( ldvl, *
       )VL, integerLDVL, double precision, dimension( ldvr, * )VR, integerLDVR, integerMM,
       integerM, double precision, dimension( * )WORK, integerINFO)
       DTREVC

       Purpose:

            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**T)*T = w*(y**T)

            where y**T denotes the 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.

       Parameters:
           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

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       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|.

       Definition at line 222 of file dtrevc.f.

Author

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