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

NAME

       LAPACK-3 - computes the eigenvectors of the tridiagonal matrix T = L D L**T given L, D and
       APPROXIMATIONS to the eigenvalues of L D L**T

SYNOPSIS

       SUBROUTINE ZLARRV( N, VL, VU, D, L, PIVMIN, ISPLIT, M, DOL, DOU, MINRGP, RTOL1, RTOL2,  W,
                          WERR, WGAP, IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ, WORK, IWORK, INFO )

           INTEGER        DOL, DOU, INFO, LDZ, M, N

           DOUBLE         PRECISION MINRGP, PIVMIN, RTOL1, RTOL2, VL, VU

           INTEGER        IBLOCK( * ), INDEXW( * ), ISPLIT( * ), ISUPPZ( * ), IWORK( * )

           DOUBLE         PRECISION  D(  *  ),  GERS(  * ), L( * ), W( * ), WERR( * ), WGAP( * ),
                          WORK( * )

           COMPLEX*16     Z( LDZ, * )

PURPOSE

       ZLARRV computes the eigenvectors of the tridiagonal matrix T = L D L**T  given  L,  D  and
       APPROXIMATIONS to the eigenvalues of L D L**T.
        The input eigenvalues should have been computed by DLARRE.

ARGUMENTS

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

        VL      (input) DOUBLE PRECISION
                VU      (input) DOUBLE PRECISION
                Lower and upper bounds of the interval that contains the desired
                eigenvalues. VL < VU. Needed to compute gaps on the left or right
                end of the extremal eigenvalues in the desired RANGE.

        D       (input/output) DOUBLE PRECISION array, dimension (N)
                On entry, the N diagonal elements of the diagonal matrix D.
                On exit, D may be overwritten.

        L       (input/output) DOUBLE PRECISION array, dimension (N)
                On entry, the (N-1) subdiagonal elements of the unit
                bidiagonal matrix L are in elements 1 to N-1 of L
                (if the matrix is not splitted.) At the end of each block
                is stored the corresponding shift as given by DLARRE.
                On exit, L is overwritten.

        PIVMIN  (in) DOUBLE PRECISION
                The minimum pivot allowed in the Sturm sequence.

        ISPLIT  (input) INTEGER array, dimension (N)
                The splitting points, at which T breaks up into blocks.
                The first block consists of rows/columns 1 to
                ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1
                through ISPLIT( 2 ), etc.

        M       (input) INTEGER
                The total number of input eigenvalues.  0 <= M <= N.

        DOL     (input) INTEGER
                DOU     (input) INTEGER
                If the user wants to compute only selected eigenvectors from all
                the eigenvalues supplied, he can specify an index range DOL:DOU.
                Or else the setting DOL=1, DOU=M should be applied.
                Note that DOL and DOU refer to the order in which the eigenvalues
                are stored in W.
                If the user wants to compute only selected eigenpairs, then
                the columns DOL-1 to DOU+1 of the eigenvector space Z contain the
                computed eigenvectors. All other columns of Z are set to zero.

        MINRGP  (input) DOUBLE PRECISION

        RTOL1   (input) DOUBLE PRECISION
                RTOL2   (input) DOUBLE PRECISION
                Parameters for bisection.
                RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )

        W       (input/output) DOUBLE PRECISION array, dimension (N)
                The first M elements of W contain the APPROXIMATE eigenvalues for
                which eigenvectors are to be computed.  The eigenvalues
                should be grouped by split-off block and ordered from
                smallest to largest within the block ( The output array
                W from DLARRE is expected here ). Furthermore, they are with
                respect to the shift of the corresponding root representation
                for their block. On exit, W holds the eigenvalues of the
                UNshifted matrix.

        WERR    (input/output) DOUBLE PRECISION array, dimension (N)
                The first M elements contain the semiwidth of the uncertainty
                interval of the corresponding eigenvalue in W

        WGAP    (input/output) DOUBLE PRECISION array, dimension (N)
                The separation from the right neighbor eigenvalue in W.

        IBLOCK  (input) INTEGER array, dimension (N)
                The indices of the blocks (submatrices) associated with the
                corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue
                W(i) belongs to the first block from the top, =2 if W(i)
                belongs to the second block, etc.

        INDEXW  (input) INTEGER array, dimension (N)
                The indices of the eigenvalues within each block (submatrix);
                for example, INDEXW(i)= 10 and IBLOCK(i)=2 imply that the
                i-th eigenvalue W(i) is the 10-th eigenvalue in the second block.

        GERS    (input) DOUBLE PRECISION array, dimension (2*N)
                The N Gerschgorin intervals (the i-th Gerschgorin interval
                is (GERS(2*i-1), GERS(2*i)). The Gerschgorin intervals should
                be computed from the original UNshifted matrix.

        Z       (output) COMPLEX*16       array, dimension (LDZ, max(1,M) )
                If INFO = 0, the first M columns of Z contain the
                orthonormal eigenvectors of the matrix T
                corresponding to the input eigenvalues, with the i-th
                column of Z holding the eigenvector associated with W(i).
                Note: the user must ensure that at least max(1,M) columns are
                supplied in the array Z.

        LDZ     (input) INTEGER
                The leading dimension of the array Z.  LDZ >= 1, and if
                JOBZ = 'V', LDZ >= max(1,N).

        ISUPPZ  (output) INTEGER array, dimension ( 2*max(1,M) )
                The support of the eigenvectors in Z, i.e., the indices
                indicating the nonzero elements in Z. The I-th eigenvector
                is nonzero only in elements ISUPPZ( 2*I-1 ) through
                ISUPPZ( 2*I ).

        WORK    (workspace) DOUBLE PRECISION array, dimension (12*N)

        IWORK   (workspace) INTEGER array, dimension (7*N)

        INFO    (output) INTEGER
                = 0:  successful exit
                > 0:  A problem occured in ZLARRV.
                < 0:  One of the called subroutines signaled an internal problem.
                Needs inspection of the corresponding parameter IINFO
                for further information.

        =-1:  Problem in DLARRB when refining a child's eigenvalues.
              =-2:  Problem in DLARRF when computing the RRR of a child.
              When a child is inside a tight cluster, it can be difficult
              to find an RRR. A partial remedy from the user's point of
              view is to make the parameter MINRGP smaller and recompile.
              However, as the orthogonality of the computed vectors is
              proportional to 1/MINRGP, the user should be aware that
              he might be trading in precision when he decreases MINRGP.
              =-3:  Problem in DLARRB when refining a single eigenvalue
              after the Rayleigh correction was rejected.
              = 5:  The Rayleigh Quotient Iteration failed to converge to
              full accuracy in MAXITR steps.

FURTHER DETAILS

        Based on contributions by
           Beresford Parlett, University of California, Berkeley, USA
           Jim Demmel, University of California, Berkeley, USA
           Inderjit Dhillon, University of Texas, Austin, USA
           Osni Marques, LBNL/NERSC, USA
           Christof Voemel, University of California, Berkeley, USA

 LAPACK auxiliary routine (version 3.3.1)   April 2011                            ZLARRV(3lapack)