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version 1.9, 2011/11/21 22:19:31 version 1.19, 2023/08/07 08:38:54
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 *> \brief \b DLAG2  *> \brief \b DLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow.
 *  *
 *  =========== 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 DLAG2 + dependencies   *> Download DLAG2 + dependencies
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlag2.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlag2.f">
 *> [TGZ]</a>   *> [TGZ]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlag2.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlag2.f">
 *> [ZIP]</a>   *> [ZIP]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlag2.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlag2.f">
 *> [TXT]</a>  *> [TXT]</a>
 *> \endhtmlonly   *> \endhtmlonly
 *  *
 *  Definition:  *  Definition:
 *  ===========  *  ===========
 *  *
 *       SUBROUTINE DLAG2( A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1,  *       SUBROUTINE DLAG2( A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1,
 *                         WR2, WI )  *                         WR2, WI )
 *   *
 *       .. Scalar Arguments ..  *       .. Scalar Arguments ..
 *       INTEGER            LDA, LDB  *       INTEGER            LDA, LDB
 *       DOUBLE PRECISION   SAFMIN, SCALE1, SCALE2, WI, WR1, WR2  *       DOUBLE PRECISION   SAFMIN, SCALE1, SCALE2, WI, WR1, WR2
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 *       .. Array Arguments ..  *       .. Array Arguments ..
 *       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )  *       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
 *       ..  *       ..
 *    *
 *  *
 *> \par Purpose:  *> \par Purpose:
 *  =============  *  =============
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 *>          will always be positive.  If the eigenvalues are real, then  *>          will always be positive.  If the eigenvalues are real, then
 *>          the first (real) eigenvalue is  WR1 / SCALE1 , but this may  *>          the first (real) eigenvalue is  WR1 / SCALE1 , but this may
 *>          overflow or underflow, and in fact, SCALE1 may be zero or  *>          overflow or underflow, and in fact, SCALE1 may be zero or
 *>          less than the underflow threshhold if the exact eigenvalue  *>          less than the underflow threshold if the exact eigenvalue
 *>          is sufficiently large.  *>          is sufficiently large.
 *> \endverbatim  *> \endverbatim
 *>  *>
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 *>          eigenvalues are real, then the second (real) eigenvalue is  *>          eigenvalues are real, then the second (real) eigenvalue is
 *>          WR2 / SCALE2 , but this may overflow or underflow, and in  *>          WR2 / SCALE2 , but this may overflow or underflow, and in
 *>          fact, SCALE2 may be zero or less than the underflow  *>          fact, SCALE2 may be zero or less than the underflow
 *>          threshhold if the exact eigenvalue is sufficiently large.  *>          threshold if the exact eigenvalue is sufficiently large.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[out] WR1  *> \param[out] WR1
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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 DLAG2( A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1,        SUBROUTINE DLAG2( A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1,
      $                  WR2, WI )       $                  WR2, WI )
 *  *
 *  -- 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            LDA, LDB        INTEGER            LDA, LDB
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 *     Note: the test of R in the following IF is to cover the case when  *     Note: the test of R in the following IF is to cover the case when
 *           DISCR is small and negative and is flushed to zero during  *           DISCR is small and negative and is flushed to zero during
 *           the calculation of R.  On machines which have a consistent  *           the calculation of R.  On machines which have a consistent
 *           flush-to-zero threshhold and handle numbers above that  *           flush-to-zero threshold and handle numbers above that
 *           threshhold correctly, it would not be necessary.  *           threshold correctly, it would not be necessary.
 *  *
       IF( DISCR.GE.ZERO .OR. R.EQ.ZERO ) THEN        IF( DISCR.GE.ZERO .OR. R.EQ.ZERO ) THEN
          SUM = PP + SIGN( R, PP )           SUM = PP + SIGN( R, PP )
Removed from v.1.9  
changed lines
  Added in v.1.19

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