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version 1.8, 2011/11/21 20:42:55 version 1.20, 2023/08/07 08:38:54
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 *> \brief \b DLAHQR  *> \brief \b DLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm.
 *  *
 *  =========== DOCUMENTATION ===========  *  =========== DOCUMENTATION ===========
 *  *
 * Online html documentation available at   * Online html documentation available at
 *            http://www.netlib.org/lapack/explore-html/   *            http://www.netlib.org/lapack/explore-html/
 *  *
 *> \htmlonly  *> \htmlonly
 *> Download DLAHQR + dependencies   *> Download DLAHQR + dependencies
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlahqr.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlahqr.f">
 *> [TGZ]</a>   *> [TGZ]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlahqr.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlahqr.f">
 *> [ZIP]</a>   *> [ZIP]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlahqr.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlahqr.f">
 *> [TXT]</a>  *> [TXT]</a>
 *> \endhtmlonly   *> \endhtmlonly
 *  *
 *  Definition:  *  Definition:
 *  ===========  *  ===========
 *  *
 *       SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,  *       SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
 *                          ILOZ, IHIZ, Z, LDZ, INFO )  *                          ILOZ, IHIZ, Z, LDZ, INFO )
 *   *
 *       .. Scalar Arguments ..  *       .. Scalar Arguments ..
 *       INTEGER            IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N  *       INTEGER            IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
 *       LOGICAL            WANTT, WANTZ  *       LOGICAL            WANTT, WANTZ
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 *       .. Array Arguments ..  *       .. Array Arguments ..
 *       DOUBLE PRECISION   H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )  *       DOUBLE PRECISION   H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )
 *       ..  *       ..
 *    *
 *  *
 *> \par Purpose:  *> \par Purpose:
 *  =============  *  =============
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 *> \param[out] INFO  *> \param[out] INFO
 *> \verbatim  *> \verbatim
 *>          INFO is INTEGER  *>          INFO is INTEGER
 *>           =   0: successful exit  *>           = 0:  successful exit
 *>          .GT. 0: If INFO = i, DLAHQR failed to compute all the  *>           > 0:  If INFO = i, DLAHQR failed to compute all the
 *>                  eigenvalues ILO to IHI in a total of 30 iterations  *>                  eigenvalues ILO to IHI in a total of 30 iterations
 *>                  per eigenvalue; elements i+1:ihi of WR and WI  *>                  per eigenvalue; elements i+1:ihi of WR and WI
 *>                  contain those eigenvalues which have been  *>                  contain those eigenvalues which have been
 *>                  successfully computed.  *>                  successfully computed.
 *>  *>
 *>                  If INFO .GT. 0 and WANTT is .FALSE., then on exit,  *>                  If INFO > 0 and WANTT is .FALSE., then on exit,
 *>                  the remaining unconverged eigenvalues are the  *>                  the remaining unconverged eigenvalues are the
 *>                  eigenvalues of the upper Hessenberg matrix rows  *>                  eigenvalues of the upper Hessenberg matrix rows
 *>                  and columns ILO thorugh INFO of the final, output  *>                  and columns ILO through INFO of the final, output
 *>                  value of H.  *>                  value of H.
 *>  *>
 *>                  If INFO .GT. 0 and WANTT is .TRUE., then on exit  *>                  If INFO > 0 and WANTT is .TRUE., then on exit
 *>          (*)       (initial value of H)*U  = U*(final value of H)  *>          (*)       (initial value of H)*U  = U*(final value of H)
 *>                  where U is an orthognal matrix.    The final  *>                  where U is an orthogonal matrix.    The final
 *>                  value of H is upper Hessenberg and triangular in  *>                  value of H is upper Hessenberg and triangular in
 *>                  rows and columns INFO+1 through IHI.  *>                  rows and columns INFO+1 through IHI.
 *>  *>
 *>                  If INFO .GT. 0 and WANTZ is .TRUE., then on exit  *>                  If INFO > 0 and WANTZ is .TRUE., then on exit
 *>                      (final value of Z)  = (initial value of Z)*U  *>                      (final value of Z)  = (initial value of Z)*U
 *>                  where U is the orthogonal matrix in (*)  *>                  where U is the orthogonal matrix in (*)
 *>                  (regardless of the value of WANTT.)  *>                  (regardless of the value of WANTT.)
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 *  Authors:  *  Authors:
 *  ========  *  ========
 *  *
 *> \author Univ. of Tennessee   *> \author Univ. of Tennessee
 *> \author Univ. of California Berkeley   *> \author Univ. of California Berkeley
 *> \author Univ. of Colorado Denver   *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.   *> \author NAG Ltd.
 *  
 *> \date November 2011  
 *  *
 *> \ingroup doubleOTHERauxiliary  *> \ingroup doubleOTHERauxiliary
 *  *
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 *  =====================================================================  *  =====================================================================
       SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,        SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
      $                   ILOZ, IHIZ, Z, LDZ, INFO )       $                   ILOZ, IHIZ, Z, LDZ, INFO )
         IMPLICIT NONE
 *  *
 *  -- LAPACK auxiliary routine (version 3.4.0) --  *  -- LAPACK auxiliary routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2011  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N        INTEGER            IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
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 *  =========================================================  *  =========================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
       INTEGER            ITMAX  
       PARAMETER          ( ITMAX = 30 )  
       DOUBLE PRECISION   ZERO, ONE, TWO        DOUBLE PRECISION   ZERO, ONE, TWO
       PARAMETER          ( ZERO = 0.0d0, ONE = 1.0d0, TWO = 2.0d0 )        PARAMETER          ( ZERO = 0.0d0, ONE = 1.0d0, TWO = 2.0d0 )
       DOUBLE PRECISION   DAT1, DAT2        DOUBLE PRECISION   DAT1, DAT2
       PARAMETER          ( DAT1 = 3.0d0 / 4.0d0, DAT2 = -0.4375d0 )        PARAMETER          ( DAT1 = 3.0d0 / 4.0d0, DAT2 = -0.4375d0 )
         INTEGER            KEXSH
         PARAMETER          ( KEXSH = 10 )
 *     ..  *     ..
 *     .. Local Scalars ..  *     .. Local Scalars ..
       DOUBLE PRECISION   AA, AB, BA, BB, CS, DET, H11, H12, H21, H21S,        DOUBLE PRECISION   AA, AB, BA, BB, CS, DET, H11, H12, H21, H21S,
      $                   H22, RT1I, RT1R, RT2I, RT2R, RTDISC, S, SAFMAX,       $                   H22, RT1I, RT1R, RT2I, RT2R, RTDISC, S, SAFMAX,
      $                   SAFMIN, SMLNUM, SN, SUM, T1, T2, T3, TR, TST,       $                   SAFMIN, SMLNUM, SN, SUM, T1, T2, T3, TR, TST,
      $                   ULP, V2, V3       $                   ULP, V2, V3
       INTEGER            I, I1, I2, ITS, J, K, L, M, NH, NR, NZ        INTEGER            I, I1, I2, ITS, ITMAX, J, K, L, M, NH, NR, NZ,
        $                   KDEFL 
 *     ..  *     ..
 *     .. Local Arrays ..  *     .. Local Arrays ..
       DOUBLE PRECISION   V( 3 )        DOUBLE PRECISION   V( 3 )
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          I2 = N           I2 = N
       END IF        END IF
 *  *
   *     ITMAX is the total number of QR iterations allowed.
   *
         ITMAX = 30 * MAX( 10, NH )
   *
   *     KDEFL counts the number of iterations since a deflation
   *
         KDEFL = 0
   *
 *     The main loop begins here. I is the loop index and decreases from  *     The main loop begins here. I is the loop index and decreases from
 *     IHI to ILO in steps of 1 or 2. Each iteration of the loop works  *     IHI to ILO in steps of 1 or 2. Each iteration of the loop works
 *     with the active submatrix in rows and columns L to I.  *     with the active submatrix in rows and columns L to I.
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 *  *
          IF( L.GE.I-1 )           IF( L.GE.I-1 )
      $      GO TO 150       $      GO TO 150
            KDEFL = KDEFL + 1
 *  *
 *        Now the active submatrix is in rows and columns L to I. If  *        Now the active submatrix is in rows and columns L to I. If
 *        eigenvalues only are being computed, only the active submatrix  *        eigenvalues only are being computed, only the active submatrix
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             I2 = I              I2 = I
          END IF           END IF
 *  *
          IF( ITS.EQ.10 ) THEN           IF( MOD(KDEFL,2*KEXSH).EQ.0 ) THEN
 *  *
 *           Exceptional shift.  *           Exceptional shift.
 *  *
             S = ABS( H( L+1, L ) ) + ABS( H( L+2, L+1 ) )              S = ABS( H( I, I-1 ) ) + ABS( H( I-1, I-2 ) )
             H11 = DAT1*S + H( L, L )              H11 = DAT1*S + H( I, I )
             H12 = DAT2*S              H12 = DAT2*S
             H21 = S              H21 = S
             H22 = H11              H22 = H11
          ELSE IF( ITS.EQ.20 ) THEN           ELSE IF( MOD(KDEFL,KEXSH).EQ.0 ) THEN
 *  *
 *           Exceptional shift.  *           Exceptional shift.
 *  *
             S = ABS( H( I, I-1 ) ) + ABS( H( I-1, I-2 ) )              S = ABS( H( L+1, L ) ) + ABS( H( L+2, L+1 ) )
             H11 = DAT1*S + H( I, I )              H11 = DAT1*S + H( L, L )
             H12 = DAT2*S              H12 = DAT2*S
             H21 = S              H21 = S
             H22 = H11              H22 = H11
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             CALL DROT( NZ, Z( ILOZ, I-1 ), 1, Z( ILOZ, I ), 1, CS, SN )              CALL DROT( NZ, Z( ILOZ, I-1 ), 1, Z( ILOZ, I ), 1, CS, SN )
          END IF           END IF
       END IF        END IF
   *     reset deflation counter
         KDEFL = 0
 *  *
 *     return to start of the main loop with new value of I.  *     return to start of the main loop with new value of I.
 *  *
Removed from v.1.8  
changed lines
  Added in v.1.20

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