Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  computes some or all of the right and/or left eigenvectors of a complex upper
       triangular matrix T

SYNOPSIS

       SUBROUTINE ZTREVC( 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( * )

           DOUBLE         PRECISION RWORK( * )

           COMPLEX*16     T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ), WORK( * )

PURPOSE

       ZTREVC  computes  some  or  all  of  the right and/or left eigenvectors of a complex upper
       triangular matrix T.
        Matrices of this type are produced by the Schur factorization of
        a complex general matrix:  A = Q*T*Q**H, as computed by ZHSEQR.

        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 the vector y.
        The eigenvalues are not input to this routine, but are read directly
        from the diagonal 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 unitary 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.

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,
                backtransformed using the matrices supplied in
                VR and/or VL;
                = 'S':  compute selected right and/or left eigenvectors,
                as indicated by the logical array SELECT.

        SELECT  (input) LOGICAL array, dimension (N)
                If HOWMNY = 'S', SELECT specifies the eigenvectors to be
                computed.
                The eigenvector corresponding to the j-th eigenvalue is
                computed if SELECT(j) = .TRUE..
                Not referenced if HOWMNY = 'A' or 'B'.

        N       (input) INTEGER
                The order of the matrix T. N >= 0.

        T       (input/output) COMPLEX*16 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*16 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 ZHSEQR).
                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.
                Not referenced if SIDE = 'R'.

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

        VR      (input/output) COMPLEX*16 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 ZHSEQR).
                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.
                Not referenced if SIDE = 'L'.

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

        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*16 array, dimension (2*N)

        RWORK   (workspace) DOUBLE PRECISION array, dimension (N)

        INFO    (output) INTEGER
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th 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 routine (version 3.3.1)             April 2011                            ZTREVC(3lapack)