clahqr(3S)

NAME
     CLAHQR - 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 CLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z,
                        LDZ, INFO )

         LOGICAL        WANTT, WANTZ

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

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

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     CLAHQR 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).  CLAHQR 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 array, dimension (LDH,N)
             On entry, the upper Hessenberg matrix H.  On exit, if WANTT is
             .TRUE., H is upper 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).

     W       (output) COMPLEX 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 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
             > 0: if INFO = i, CLAHQR failed to compute all the eigenvalues
             ILO to IHI in a total of 30*(IHI-ILO+1) iterations; elements
             i+1:ihi of W contain those eigenvalues which have been
             successfully computed.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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