version 1.7, 2010/12/21 13:53:33
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version 1.21, 2023/08/07 08:38:59
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SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, |
*> \brief \b DLASQ4 computes an approximation to the smallest eigenvalue using values of d from the previous transform. Used by sbdsqr. |
$ DN1, DN2, TAU, TTYPE, G ) |
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* |
* |
* -- LAPACK routine (version 3.2) -- |
* =========== DOCUMENTATION =========== |
* |
* |
* -- Contributed by Osni Marques of the Lawrence Berkeley National -- |
* Online html documentation available at |
* -- Laboratory and Beresford Parlett of the Univ. of California at -- |
* http://www.netlib.org/lapack/explore-html/ |
* -- Berkeley -- |
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* -- November 2008 -- |
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* |
* |
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*> \htmlonly |
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*> Download DLASQ4 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq4.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq4.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq4.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, |
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* DN1, DN2, TAU, TTYPE, G ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER I0, N0, N0IN, PP, TTYPE |
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* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION Z( * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> DLASQ4 computes an approximation TAU to the smallest eigenvalue |
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*> using values of d from the previous transform. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] I0 |
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*> \verbatim |
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*> I0 is INTEGER |
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*> First index. |
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*> \endverbatim |
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*> |
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*> \param[in] N0 |
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*> \verbatim |
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*> N0 is INTEGER |
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*> Last index. |
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*> \endverbatim |
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*> |
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*> \param[in] Z |
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*> \verbatim |
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*> Z is DOUBLE PRECISION array, dimension ( 4*N0 ) |
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*> Z holds the qd array. |
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*> \endverbatim |
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*> |
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*> \param[in] PP |
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*> \verbatim |
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*> PP is INTEGER |
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*> PP=0 for ping, PP=1 for pong. |
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*> \endverbatim |
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*> |
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*> \param[in] N0IN |
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*> \verbatim |
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*> N0IN is INTEGER |
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*> The value of N0 at start of EIGTEST. |
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*> \endverbatim |
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*> |
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*> \param[in] DMIN |
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*> \verbatim |
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*> DMIN is DOUBLE PRECISION |
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*> Minimum value of d. |
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*> \endverbatim |
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*> |
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*> \param[in] DMIN1 |
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*> \verbatim |
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*> DMIN1 is DOUBLE PRECISION |
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*> Minimum value of d, excluding D( N0 ). |
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*> \endverbatim |
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*> |
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*> \param[in] DMIN2 |
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*> \verbatim |
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*> DMIN2 is DOUBLE PRECISION |
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*> Minimum value of d, excluding D( N0 ) and D( N0-1 ). |
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*> \endverbatim |
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*> |
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*> \param[in] DN |
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*> \verbatim |
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*> DN is DOUBLE PRECISION |
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*> d(N) |
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*> \endverbatim |
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*> |
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*> \param[in] DN1 |
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*> \verbatim |
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*> DN1 is DOUBLE PRECISION |
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*> d(N-1) |
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*> \endverbatim |
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*> |
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*> \param[in] DN2 |
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*> \verbatim |
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*> DN2 is DOUBLE PRECISION |
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*> d(N-2) |
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*> \endverbatim |
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*> |
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*> \param[out] TAU |
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*> \verbatim |
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*> TAU is DOUBLE PRECISION |
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*> This is the shift. |
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*> \endverbatim |
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*> |
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*> \param[out] TTYPE |
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*> \verbatim |
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*> TTYPE is INTEGER |
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*> Shift type. |
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*> \endverbatim |
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*> |
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*> \param[in,out] G |
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*> \verbatim |
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*> G is DOUBLE PRECISION |
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*> G is passed as an argument in order to save its value between |
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*> calls to DLASQ4. |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \ingroup auxOTHERcomputational |
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* |
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*> \par Further Details: |
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* ===================== |
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*> |
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*> \verbatim |
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*> |
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*> CNST1 = 9/16 |
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*> \endverbatim |
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*> |
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* ===================================================================== |
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SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, |
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$ DN1, DN2, TAU, TTYPE, G ) |
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* |
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* -- LAPACK computational 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..-- |
* |
* |
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DOUBLE PRECISION Z( * ) |
DOUBLE PRECISION Z( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DLASQ4 computes an approximation TAU to the smallest eigenvalue |
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* using values of d from the previous transform. |
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* |
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* I0 (input) INTEGER |
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* First index. |
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* |
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* N0 (input) INTEGER |
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* Last index. |
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* |
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* Z (input) DOUBLE PRECISION array, dimension ( 4*N ) |
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* Z holds the qd array. |
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* |
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* PP (input) INTEGER |
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* PP=0 for ping, PP=1 for pong. |
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* |
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* NOIN (input) INTEGER |
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* The value of N0 at start of EIGTEST. |
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* |
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* DMIN (input) DOUBLE PRECISION |
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* Minimum value of d. |
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* |
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* DMIN1 (input) DOUBLE PRECISION |
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* Minimum value of d, excluding D( N0 ). |
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* |
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* DMIN2 (input) DOUBLE PRECISION |
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* Minimum value of d, excluding D( N0 ) and D( N0-1 ). |
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* |
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* DN (input) DOUBLE PRECISION |
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* d(N) |
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* |
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* DN1 (input) DOUBLE PRECISION |
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* d(N-1) |
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* |
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* DN2 (input) DOUBLE PRECISION |
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* d(N-2) |
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* |
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* TAU (output) DOUBLE PRECISION |
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* This is the shift. |
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* |
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* TTYPE (output) INTEGER |
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* Shift type. |
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* |
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* G (input/output) REAL |
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* G is passed as an argument in order to save its value between |
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* calls to DLASQ4. |
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* |
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* Further Details |
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* =============== |
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* CNST1 = 9/16 |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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TTYPE = -1 |
TTYPE = -1 |
RETURN |
RETURN |
END IF |
END IF |
* |
* |
NN = 4*N0 + PP |
NN = 4*N0 + PP |
IF( N0IN.EQ.N0 ) THEN |
IF( N0IN.EQ.N0 ) THEN |
* |
* |
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NP = NN - 9 |
NP = NN - 9 |
ELSE |
ELSE |
NP = NN - 2*PP |
NP = NN - 2*PP |
B2 = Z( NP-2 ) |
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GAM = DN1 |
GAM = DN1 |
IF( Z( NP-4 ) .GT. Z( NP-2 ) ) |
IF( Z( NP-4 ) .GT. Z( NP-2 ) ) |
$ RETURN |
$ RETURN |
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$ RETURN |
$ RETURN |
B2 = B2*( Z( I4 ) / Z( I4-2 ) ) |
B2 = B2*( Z( I4 ) / Z( I4-2 ) ) |
A2 = A2 + B2 |
A2 = A2 + B2 |
IF( HUNDRD*MAX( B2, B1 ).LT.A2 .OR. CNST1.LT.A2 ) |
IF( HUNDRD*MAX( B2, B1 ).LT.A2 .OR. CNST1.LT.A2 ) |
$ GO TO 20 |
$ GO TO 20 |
10 CONTINUE |
10 CONTINUE |
20 CONTINUE |
20 CONTINUE |
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$ RETURN |
$ RETURN |
B2 = B2*( Z( I4 ) / Z( I4-2 ) ) |
B2 = B2*( Z( I4 ) / Z( I4-2 ) ) |
A2 = A2 + B2 |
A2 = A2 + B2 |
IF( HUNDRD*MAX( B2, B1 ).LT.A2 .OR. CNST1.LT.A2 ) |
IF( HUNDRD*MAX( B2, B1 ).LT.A2 .OR. CNST1.LT.A2 ) |
$ GO TO 40 |
$ GO TO 40 |
30 CONTINUE |
30 CONTINUE |
40 CONTINUE |
40 CONTINUE |
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* |
* |
* One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN. |
* One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN. |
* |
* |
IF( DMIN1.EQ.DN1 .AND. DMIN2.EQ.DN2 ) THEN |
IF( DMIN1.EQ.DN1 .AND. DMIN2.EQ.DN2 ) THEN |
* |
* |
* Cases 7 and 8. |
* Cases 7 and 8. |
* |
* |
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$ RETURN |
$ RETURN |
B1 = B1*( Z( I4 ) / Z( I4-2 ) ) |
B1 = B1*( Z( I4 ) / Z( I4-2 ) ) |
B2 = B2 + B1 |
B2 = B2 + B1 |
IF( HUNDRD*MAX( B1, A2 ).LT.B2 ) |
IF( HUNDRD*MAX( B1, A2 ).LT.B2 ) |
$ GO TO 60 |
$ GO TO 60 |
50 CONTINUE |
50 CONTINUE |
60 CONTINUE |
60 CONTINUE |
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GAP2 = HALF*DMIN2 - A2 |
GAP2 = HALF*DMIN2 - A2 |
IF( GAP2.GT.ZERO .AND. GAP2.GT.B2*A2 ) THEN |
IF( GAP2.GT.ZERO .AND. GAP2.GT.B2*A2 ) THEN |
S = MAX( S, A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ) ) |
S = MAX( S, A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ) ) |
ELSE |
ELSE |
S = MAX( S, A2*( ONE-CNST2*B2 ) ) |
S = MAX( S, A2*( ONE-CNST2*B2 ) ) |
TTYPE = -8 |
TTYPE = -8 |
END IF |
END IF |
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* |
* |
* Cases 10 and 11. |
* Cases 10 and 11. |
* |
* |
IF( DMIN2.EQ.DN2 .AND. TWO*Z( NN-5 ).LT.Z( NN-7 ) ) THEN |
IF( DMIN2.EQ.DN2 .AND. TWO*Z( NN-5 ).LT.Z( NN-7 ) ) THEN |
TTYPE = -10 |
TTYPE = -10 |
S = THIRD*DMIN2 |
S = THIRD*DMIN2 |
IF( Z( NN-5 ).GT.Z( NN-7 ) ) |
IF( Z( NN-5 ).GT.Z( NN-7 ) ) |
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$ SQRT( Z( NN-11 ) )*SQRT( Z( NN-9 ) ) - A2 |
$ SQRT( Z( NN-11 ) )*SQRT( Z( NN-9 ) ) - A2 |
IF( GAP2.GT.ZERO .AND. GAP2.GT.B2*A2 ) THEN |
IF( GAP2.GT.ZERO .AND. GAP2.GT.B2*A2 ) THEN |
S = MAX( S, A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ) ) |
S = MAX( S, A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ) ) |
ELSE |
ELSE |
S = MAX( S, A2*( ONE-CNST2*B2 ) ) |
S = MAX( S, A2*( ONE-CNST2*B2 ) ) |
END IF |
END IF |
ELSE |
ELSE |
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* |
* |
* Case 12, more than two eigenvalues deflated. No information. |
* Case 12, more than two eigenvalues deflated. No information. |
* |
* |
S = ZERO |
S = ZERO |
TTYPE = -12 |
TTYPE = -12 |
END IF |
END IF |
* |
* |