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version 1.8, 2011/11/21 20:43:12 version 1.19, 2018/05/29 07:18:21
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 *  *
 *  =========== 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 ZHGEQZ + dependencies   *> Download ZHGEQZ + dependencies
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhgeqz.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhgeqz.f">
 *> [TGZ]</a>   *> [TGZ]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhgeqz.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhgeqz.f">
 *> [ZIP]</a>   *> [ZIP]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhgeqz.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhgeqz.f">
 *> [TXT]</a>  *> [TXT]</a>
 *> \endhtmlonly   *> \endhtmlonly
 *  *
 *  Definition:  *  Definition:
 *  ===========  *  ===========
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 *       SUBROUTINE ZHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,  *       SUBROUTINE ZHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
 *                          ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK,  *                          ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK,
 *                          RWORK, INFO )  *                          RWORK, INFO )
 *   *
 *       .. Scalar Arguments ..  *       .. Scalar Arguments ..
 *       CHARACTER          COMPQ, COMPZ, JOB  *       CHARACTER          COMPQ, COMPZ, JOB
 *       INTEGER            IHI, ILO, INFO, LDH, LDQ, LDT, LDZ, LWORK, N  *       INTEGER            IHI, ILO, INFO, LDH, LDQ, LDT, LDZ, LWORK, N
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 *      $                   Q( LDQ, * ), T( LDT, * ), WORK( * ),  *      $                   Q( LDQ, * ), T( LDT, * ), WORK( * ),
 *      $                   Z( LDZ, * )  *      $                   Z( LDZ, * )
 *       ..  *       ..
 *    *
 *  *
 *> \par Purpose:  *> \par Purpose:
 *  =============  *  =============
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 *> using the single-shift QZ method.  *> using the single-shift QZ method.
 *> Matrix pairs of this type are produced by the reduction to  *> Matrix pairs of this type are produced by the reduction to
 *> generalized upper Hessenberg form of a complex matrix pair (A,B):  *> generalized upper Hessenberg form of a complex matrix pair (A,B):
 *>   *>
 *>    A = Q1*H*Z1**H,  B = Q1*T*Z1**H,  *>    A = Q1*H*Z1**H,  B = Q1*T*Z1**H,
 *>   *>
 *> as computed by ZGGHRD.  *> as computed by ZGGHRD.
 *>   *>
 *> If JOB='S', then the Hessenberg-triangular pair (H,T) is  *> If JOB='S', then the Hessenberg-triangular pair (H,T) is
 *> also reduced to generalized Schur form,  *> also reduced to generalized Schur form,
 *>   *>
 *>    H = Q*S*Z**H,  T = Q*P*Z**H,  *>    H = Q*S*Z**H,  T = Q*P*Z**H,
 *>   *>
 *> where Q and Z are unitary matrices and S and P are upper triangular.  *> where Q and Z are unitary matrices and S and P are upper triangular.
 *>   *>
 *> Optionally, the unitary matrix Q from the generalized Schur  *> Optionally, the unitary matrix Q from the generalized Schur
 *> factorization may be postmultiplied into an input matrix Q1, and the  *> factorization may be postmultiplied into an input matrix Q1, and the
 *> unitary matrix Z may be postmultiplied into an input matrix Z1.  *> unitary matrix Z may be postmultiplied into an input matrix Z1.
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 *> the matrix pair (A,B) to generalized Hessenberg form, then the output  *> the matrix pair (A,B) to generalized Hessenberg form, then the output
 *> matrices Q1*Q and Z1*Z are the unitary factors from the generalized  *> matrices Q1*Q and Z1*Z are the unitary factors from the generalized
 *> Schur factorization of (A,B):  *> Schur factorization of (A,B):
 *>   *>
 *>    A = (Q1*Q)*S*(Z1*Z)**H,  B = (Q1*Q)*P*(Z1*Z)**H.  *>    A = (Q1*Q)*S*(Z1*Z)**H,  B = (Q1*Q)*P*(Z1*Z)**H.
 *>   *>
 *> To avoid overflow, eigenvalues of the matrix pair (H,T)  *> To avoid overflow, eigenvalues of the matrix pair (H,T)
 *> (equivalently, of (A,B)) are computed as a pair of complex values  *> (equivalently, of (A,B)) are computed as a pair of complex values
 *> (alpha,beta).  If beta is nonzero, lambda = alpha / beta is an  *> (alpha,beta).  If beta is nonzero, lambda = alpha / beta is an
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 *> \param[in,out] Q  *> \param[in,out] Q
 *> \verbatim  *> \verbatim
 *>          Q is COMPLEX*16 array, dimension (LDQ, N)  *>          Q is COMPLEX*16 array, dimension (LDQ, N)
 *>          On entry, if COMPZ = 'V', the unitary matrix Q1 used in the  *>          On entry, if COMPQ = 'V', the unitary matrix Q1 used in the
 *>          reduction of (A,B) to generalized Hessenberg form.  *>          reduction of (A,B) to generalized Hessenberg form.
 *>          On exit, if COMPZ = 'I', the unitary matrix of left Schur  *>          On exit, if COMPQ = 'I', the unitary matrix of left Schur
 *>          vectors of (H,T), and if COMPZ = 'V', the unitary matrix of  *>          vectors of (H,T), and if COMPQ = 'V', the unitary matrix of
 *>          left Schur vectors of (A,B).  *>          left Schur vectors of (A,B).
 *>          Not referenced if COMPZ = 'N'.  *>          Not referenced if COMPQ = 'N'.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] LDQ  *> \param[in] LDQ
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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  *> \date April 2012
 *  *
 *> \ingroup complex16GEcomputational  *> \ingroup complex16GEcomputational
 *  *
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      $                   ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK,       $                   ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK,
      $                   RWORK, INFO )       $                   RWORK, INFO )
 *  *
 *  -- LAPACK computational routine (version 3.4.0) --  *  -- LAPACK computational routine (version 3.7.0) --
 *  -- 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  *     April 2012
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          COMPQ, COMPZ, JOB        CHARACTER          COMPQ, COMPZ, JOB
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                CALL ZSCAL( J-1, SIGNBC, T( 1, J ), 1 )                 CALL ZSCAL( J-1, SIGNBC, T( 1, J ), 1 )
                CALL ZSCAL( J, SIGNBC, H( 1, J ), 1 )                 CALL ZSCAL( J, SIGNBC, H( 1, J ), 1 )
             ELSE              ELSE
                H( J, J ) = H( J, J )*SIGNBC                 CALL ZSCAL( 1, SIGNBC, H( J, J ), 1 )
             END IF              END IF
             IF( ILZ )              IF( ILZ )
      $         CALL ZSCAL( N, SIGNBC, Z( 1, J ), 1 )       $         CALL ZSCAL( N, SIGNBC, Z( 1, J ), 1 )
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                CALL ZSCAL( ILAST+1-IFRSTM, SIGNBC, H( IFRSTM, ILAST ),                 CALL ZSCAL( ILAST+1-IFRSTM, SIGNBC, H( IFRSTM, ILAST ),
      $                     1 )       $                     1 )
             ELSE              ELSE
                H( ILAST, ILAST ) = H( ILAST, ILAST )*SIGNBC                 CALL ZSCAL( 1, SIGNBC, H( ILAST, ILAST ), 1 )
             END IF              END IF
             IF( ILZ )              IF( ILZ )
      $         CALL ZSCAL( N, SIGNBC, Z( 1, ILAST ), 1 )       $         CALL ZSCAL( N, SIGNBC, Z( 1, ILAST ), 1 )
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 *  *
 *           Exceptional shift.  Chosen for no particularly good reason.  *           Exceptional shift.  Chosen for no particularly good reason.
 *  *
             ESHIFT = ESHIFT + DCONJG( ( ASCALE*H( ILAST-1, ILAST ) ) /              ESHIFT = ESHIFT + (ASCALE*H(ILAST,ILAST-1))/
      $               ( BSCALE*T( ILAST-1, ILAST-1 ) ) )       $                        (BSCALE*T(ILAST-1,ILAST-1))
             SHIFT = ESHIFT              SHIFT = ESHIFT
          END IF           END IF
 *  *
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                CALL ZSCAL( J-1, SIGNBC, T( 1, J ), 1 )                 CALL ZSCAL( J-1, SIGNBC, T( 1, J ), 1 )
                CALL ZSCAL( J, SIGNBC, H( 1, J ), 1 )                 CALL ZSCAL( J, SIGNBC, H( 1, J ), 1 )
             ELSE              ELSE
                H( J, J ) = H( J, J )*SIGNBC                 CALL ZSCAL( 1, SIGNBC, H( J, J ), 1 )
             END IF              END IF
             IF( ILZ )              IF( ILZ )
      $         CALL ZSCAL( N, SIGNBC, Z( 1, J ), 1 )       $         CALL ZSCAL( N, SIGNBC, Z( 1, J ), 1 )
Removed from v.1.8  
changed lines
  Added in v.1.19

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