slahqr(3S)

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, * )

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
     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 corresponding 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; 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: 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 computed.

FURTHER DETAILS
     2-96 Based on modifications by
        David Day, Sandia National Laboratory, USA


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

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