Previous: slagts Up: ../lapack-s.html Next: slahrd

slahqr

 NAME
      SLAHQR - i an auxiliary routine called by SHSEQR to update
      the eigenvalues and Schur decomposition already computed by
      SHSEQR, by dealing with the Hessenberg submatrix in rows and
      columns ILO to IHI

 SYNOPSIS
      SUBROUTINE SLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR,
                         WI, ILOZ, IHIZ, Z, LDZ, INFO )

          LOGICAL        WANTT, WANTZ

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

          REAL           H( LDH, * ), WI( * ), WR( * ), Z( LDZ, *
                         )

 PURPOSE
      SLAHQR is an auxiliary routine called by SHSEQR to update
      the eigenvalues and Schur decomposition already computed by
      SHSEQR, 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 quasi-triangular in rows and columns
              IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1).
              SLAHQR 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) REAL array, dimension (LDH,N)
              On entry, the upper Hessenberg matrix H.  On exit,
              if WANTT is .TRUE., H is upper quasi-triangular in
              rows and columns ILO:IHI, with any 2-by-2 diagonal
              blocks in standard form. If WANTT is .FALSE., the
              contents of H are unspecified on exit.

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

      WR      (output) REAL array, dimension (N)
              WI      (output) REAL array, dimension (N) The real
              and imaginary parts, respectively, of the computed
              eigenvalues ILO to IHI are stored in the correspond-
              ing elements of WR and WI. If two eigenvalues are
              computed as a complex conjugate pair, they are
              stored in consecutive elements of WR and WI, say the
              i-th and (i+1)th, with WI(i) > 0 and WI(i+1) < 0. If
              WANTT is .TRUE., the eigenvalues are stored in the
              same order as on the diagonal of the Schur form
              returned in H, with WR(i) = H(i,i), and, if
              H(i:i+1,i:i+1) is a 2-by-2 diagonal block, WI(i) =
              sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(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) REAL array, dimension (LDZ,N)
              If WANTZ is .TRUE., on entry Z must contain the
              current matrix Z of transformations accumulated by
              SHSEQR, and on exit Z has been updated; transforma-
              tions 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
              > 0: SLAHQR failed to compute all the eigenvalues
              ILO to IHI in a total of 30*(IHI-ILO+1) iterations;
              if INFO = i, elements i+1:ihi of WR and WI contain
              those eigenvalues which have been successfully com-
              puted.