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

NAME

       LAPACK-3  -  ZLAHQR i an auxiliary routine called by CHSEQR to update the  eigenvalues and
       Schur decomposition already computed by CHSEQR, by  dealing with the Hessenberg  submatrix
       in rows and columns ILO to  IHI

SYNOPSIS

       SUBROUTINE ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z, LDZ, INFO )

           INTEGER        IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N

           LOGICAL        WANTT, WANTZ

           COMPLEX*16     H( LDH, * ), W( * ), Z( LDZ, * )

PURPOSE

          ZLAHQR is an auxiliary routine called by CHSEQR to update the
          eigenvalues and Schur decomposition already computed by CHSEQR, by
          dealing with the Hessenberg submatrix in rows and columns ILO to
          IHI.

ARGUMENTS

        WANTT   (input) LOGICAL
                = .TRUE. : the full Schur form T is required;
                = .FALSE.: only eigenvalues are required.

        WANTZ   (input) LOGICAL
                = .TRUE. : the matrix of Schur vectors Z is required;
                = .FALSE.: Schur vectors are not required.

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

        ILO     (input) INTEGER
                IHI     (input) INTEGER
                It is assumed that H is already upper triangular in rows and
                columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1).
                ZLAHQR works primarily with the Hessenberg submatrix in rows
                and columns ILO to IHI, but applies transformations to all of
                H if WANTT is .TRUE..
                1 <= ILO <= max(1,IHI); IHI <= N.

        H       (input/output) COMPLEX*16 array, dimension (LDH,N)
                On entry, the upper Hessenberg matrix H.
                On exit, if INFO is zero and if WANTT is .TRUE., then H
                is upper triangular in rows and columns ILO:IHI.  If INFO
                is zero and if WANTT is .FALSE., then the contents of H
                are unspecified on exit.  The output state of H in case
                INF is positive is below under the description of INFO.

        LDH     (input) INTEGER
                The leading dimension of the array H. LDH >= max(1,N).

        W       (output) COMPLEX*16 array, dimension (N)
                The computed eigenvalues ILO to IHI are stored in the
                corresponding elements of W. If WANTT is .TRUE., the
                eigenvalues are stored in the same order as on the diagonal
                of the Schur form returned in H, with W(i) = H(i,i).

        ILOZ    (input) INTEGER
                IHIZ    (input) INTEGER
                Specify the rows of Z to which transformations must be
                applied if WANTZ is .TRUE..
                1 <= ILOZ <= ILO; IHI <= IHIZ <= N.

        Z       (input/output) COMPLEX*16 array, dimension (LDZ,N)
                If WANTZ is .TRUE., on entry Z must contain the current
                matrix Z of transformations accumulated by CHSEQR, and on
                exit Z has been updated; transformations are applied only to
                the submatrix Z(ILOZ:IHIZ,ILO:IHI).
                If WANTZ is .FALSE., Z is not referenced.

        LDZ     (input) INTEGER
                The leading dimension of the array Z. LDZ >= max(1,N).

        INFO    (output) INTEGER
                =   0: successful exit
                .GT. 0: if INFO = i, ZLAHQR failed to compute all the
                eigenvalues ILO to IHI in a total of 30 iterations
                per eigenvalue; elements i+1:ihi of W contain
                those eigenvalues which have been successfully
                computed.
                If INFO .GT. 0 and WANTT is .FALSE., then on exit,
                the remaining unconverged eigenvalues are the
                eigenvalues of the upper Hessenberg matrix
                rows and columns ILO thorugh INFO of the final,
                output value of H.
                If INFO .GT. 0 and WANTT is .TRUE., then on exit
                (*)       (initial value of H)*U  = U*(final value of H)
                where U is an orthognal matrix.    The final
                value of H is upper Hessenberg and triangular in
                rows and columns INFO+1 through IHI.
                If INFO .GT. 0 and WANTZ is .TRUE., then on exit
                (final value of Z)  = (initial value of Z)*U
                where U is the orthogonal matrix in (*)
                (regardless of the value of WANTT.)

FURTHER DETAILS

           02-96 Based on modifications by
           David Day, Sandia National Laboratory, USA
           12-04 Further modifications by
           Ralph Byers, University of Kansas, USA
           This is a modified version of ZLAHQR from LAPACK version 3.0.
           It is (1) more robust against overflow and underflow and
           (2) adopts the more conservative Ahues & Tisseur stopping
           criterion (LAWN 122, 1997).

 LAPACK auxiliary routine (version 3.2)     April 2011                            ZLAHQR(3lapack)