version 1.3, 2010/08/06 15:28:43
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version 1.19, 2018/05/29 07:18:01
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SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, DMIN, DMIN1, DMIN2, DN, |
*> \brief \b DLASQ5 computes one dqds transform in ping-pong form. Used by sbdsqr and sstegr. |
$ DNM1, DNM2, IEEE ) |
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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 DLASQ5 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq5.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/dlasq5.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/dlasq5.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 DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, DN, |
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* DNM1, DNM2, IEEE, EPS ) |
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* |
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* .. Scalar Arguments .. |
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* LOGICAL IEEE |
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* INTEGER I0, N0, PP |
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* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU, SIGMA, EPS |
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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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*> DLASQ5 computes one dqds transform in ping-pong form, one |
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*> version for IEEE machines another for non IEEE machines. |
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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*N ) |
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*> Z holds the qd array. EMIN is stored in Z(4*N0) to avoid |
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*> an extra argument. |
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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] 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[in] SIGMA |
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*> \verbatim |
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*> SIGMA is DOUBLE PRECISION |
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*> This is the accumulated shift up to this step. |
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*> \endverbatim |
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*> |
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*> \param[out] 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[out] 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[out] 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[out] DN |
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*> \verbatim |
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*> DN is DOUBLE PRECISION |
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*> d(N0), the last value of d. |
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*> \endverbatim |
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*> |
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*> \param[out] DNM1 |
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*> \verbatim |
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*> DNM1 is DOUBLE PRECISION |
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*> d(N0-1). |
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*> \endverbatim |
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*> |
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*> \param[out] DNM2 |
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*> \verbatim |
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*> DNM2 is DOUBLE PRECISION |
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*> d(N0-2). |
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*> \endverbatim |
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*> |
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*> \param[in] IEEE |
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*> \verbatim |
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*> IEEE is LOGICAL |
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*> Flag for IEEE or non IEEE arithmetic. |
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*> \endverbatim |
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*> |
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*> \param[in] EPS |
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*> \verbatim |
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*> EPS is DOUBLE PRECISION |
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*> This is the value of epsilon used. |
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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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*> \date June 2017 |
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* |
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*> \ingroup auxOTHERcomputational |
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* |
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* ===================================================================== |
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SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, |
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$ DN, DNM1, DNM2, IEEE, EPS ) |
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* |
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* -- LAPACK computational routine (version 3.7.1) -- |
* -- 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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* June 2017 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
LOGICAL IEEE |
LOGICAL IEEE |
INTEGER I0, N0, PP |
INTEGER I0, N0, PP |
DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU |
DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU, |
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$ SIGMA, EPS |
* .. |
* .. |
* .. Array Arguments .. |
* .. Array Arguments .. |
DOUBLE PRECISION Z( * ) |
DOUBLE PRECISION Z( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DLASQ5 computes one dqds transform in ping-pong form, one |
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* version for IEEE machines another for non IEEE machines. |
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* |
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* Arguments |
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* ========= |
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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. EMIN is stored in Z(4*N0) to avoid |
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* an extra argument. |
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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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* TAU (input) DOUBLE PRECISION |
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* This is the shift. |
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* |
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* DMIN (output) DOUBLE PRECISION |
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* Minimum value of d. |
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* |
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* DMIN1 (output) DOUBLE PRECISION |
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* Minimum value of d, excluding D( N0 ). |
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* |
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* DMIN2 (output) 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 (output) DOUBLE PRECISION |
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* d(N0), the last value of d. |
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* |
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* DNM1 (output) DOUBLE PRECISION |
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* d(N0-1). |
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* |
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* DNM2 (output) DOUBLE PRECISION |
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* d(N0-2). |
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* |
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* IEEE (input) LOGICAL |
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* Flag for IEEE or non IEEE arithmetic. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameter .. |
* .. Parameter .. |
DOUBLE PRECISION ZERO |
DOUBLE PRECISION ZERO, HALF |
PARAMETER ( ZERO = 0.0D0 ) |
PARAMETER ( ZERO = 0.0D0, HALF = 0.5 ) |
* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
INTEGER J4, J4P2 |
INTEGER J4, J4P2 |
DOUBLE PRECISION D, EMIN, TEMP |
DOUBLE PRECISION D, EMIN, TEMP, DTHRESH |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC MIN |
INTRINSIC MIN |
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IF( ( N0-I0-1 ).LE.0 ) |
IF( ( N0-I0-1 ).LE.0 ) |
$ RETURN |
$ RETURN |
* |
* |
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DTHRESH = EPS*(SIGMA+TAU) |
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IF( TAU.LT.DTHRESH*HALF ) TAU = ZERO |
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IF( TAU.NE.ZERO ) THEN |
J4 = 4*I0 + PP - 3 |
J4 = 4*I0 + PP - 3 |
EMIN = Z( J4+4 ) |
EMIN = Z( J4+4 ) |
D = Z( J4 ) - TAU |
D = Z( J4 ) - TAU |
DMIN = D |
DMIN = D |
DMIN1 = -Z( J4 ) |
DMIN1 = -Z( J4 ) |
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* |
* |
IF( PP.EQ.0 ) THEN |
IF( PP.EQ.0 ) THEN |
DO 10 J4 = 4*I0, 4*( N0-3 ), 4 |
DO 10 J4 = 4*I0, 4*( N0-3 ), 4 |
Z( J4-2 ) = D + Z( J4-1 ) |
Z( J4-2 ) = D + Z( J4-1 ) |
TEMP = Z( J4+1 ) / Z( J4-2 ) |
TEMP = Z( J4+1 ) / Z( J4-2 ) |
D = D*TEMP - TAU |
D = D*TEMP - TAU |
DMIN = MIN( DMIN, D ) |
DMIN = MIN( DMIN, D ) |
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10 CONTINUE |
10 CONTINUE |
ELSE |
ELSE |
DO 20 J4 = 4*I0, 4*( N0-3 ), 4 |
DO 20 J4 = 4*I0, 4*( N0-3 ), 4 |
Z( J4-3 ) = D + Z( J4 ) |
Z( J4-3 ) = D + Z( J4 ) |
TEMP = Z( J4+2 ) / Z( J4-3 ) |
TEMP = Z( J4+2 ) / Z( J4-3 ) |
D = D*TEMP - TAU |
D = D*TEMP - TAU |
DMIN = MIN( DMIN, D ) |
DMIN = MIN( DMIN, D ) |
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20 CONTINUE |
20 CONTINUE |
END IF |
END IF |
* |
* |
* Unroll last two steps. |
* Unroll last two steps. |
* |
* |
DNM2 = D |
DNM2 = D |
DMIN2 = DMIN |
DMIN2 = DMIN |
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* |
* |
IF( PP.EQ.0 ) THEN |
IF( PP.EQ.0 ) THEN |
DO 30 J4 = 4*I0, 4*( N0-3 ), 4 |
DO 30 J4 = 4*I0, 4*( N0-3 ), 4 |
Z( J4-2 ) = D + Z( J4-1 ) |
Z( J4-2 ) = D + Z( J4-1 ) |
IF( D.LT.ZERO ) THEN |
IF( D.LT.ZERO ) THEN |
RETURN |
RETURN |
ELSE |
ELSE |
Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) ) |
Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) ) |
D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU |
D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU |
END IF |
END IF |
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30 CONTINUE |
30 CONTINUE |
ELSE |
ELSE |
DO 40 J4 = 4*I0, 4*( N0-3 ), 4 |
DO 40 J4 = 4*I0, 4*( N0-3 ), 4 |
Z( J4-3 ) = D + Z( J4 ) |
Z( J4-3 ) = D + Z( J4 ) |
IF( D.LT.ZERO ) THEN |
IF( D.LT.ZERO ) THEN |
RETURN |
RETURN |
ELSE |
ELSE |
Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) ) |
Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) ) |
D = Z( J4+2 )*( D / Z( J4-3 ) ) - TAU |
D = Z( J4+2 )*( D / Z( J4-3 ) ) - TAU |
END IF |
END IF |
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40 CONTINUE |
40 CONTINUE |
END IF |
END IF |
* |
* |
* Unroll last two steps. |
* Unroll last two steps. |
* |
* |
DNM2 = D |
DNM2 = D |
DMIN2 = DMIN |
DMIN2 = DMIN |
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DMIN = MIN( DMIN, DN ) |
DMIN = MIN( DMIN, DN ) |
* |
* |
END IF |
END IF |
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ELSE |
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* This is the version that sets d's to zero if they are small enough |
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J4 = 4*I0 + PP - 3 |
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EMIN = Z( J4+4 ) |
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D = Z( J4 ) - TAU |
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DMIN = D |
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DMIN1 = -Z( J4 ) |
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IF( IEEE ) THEN |
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* |
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* Code for IEEE arithmetic. |
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* |
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IF( PP.EQ.0 ) THEN |
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DO 50 J4 = 4*I0, 4*( N0-3 ), 4 |
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Z( J4-2 ) = D + Z( J4-1 ) |
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TEMP = Z( J4+1 ) / Z( J4-2 ) |
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D = D*TEMP - TAU |
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IF( D.LT.DTHRESH ) D = ZERO |
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DMIN = MIN( DMIN, D ) |
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Z( J4 ) = Z( J4-1 )*TEMP |
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EMIN = MIN( Z( J4 ), EMIN ) |
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50 CONTINUE |
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ELSE |
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DO 60 J4 = 4*I0, 4*( N0-3 ), 4 |
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Z( J4-3 ) = D + Z( J4 ) |
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TEMP = Z( J4+2 ) / Z( J4-3 ) |
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D = D*TEMP - TAU |
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IF( D.LT.DTHRESH ) D = ZERO |
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DMIN = MIN( DMIN, D ) |
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Z( J4-1 ) = Z( J4 )*TEMP |
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EMIN = MIN( Z( J4-1 ), EMIN ) |
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60 CONTINUE |
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END IF |
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* |
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* Unroll last two steps. |
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* |
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DNM2 = D |
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DMIN2 = DMIN |
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J4 = 4*( N0-2 ) - PP |
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J4P2 = J4 + 2*PP - 1 |
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Z( J4-2 ) = DNM2 + Z( J4P2 ) |
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Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) |
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DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU |
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DMIN = MIN( DMIN, DNM1 ) |
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* |
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DMIN1 = DMIN |
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J4 = J4 + 4 |
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J4P2 = J4 + 2*PP - 1 |
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Z( J4-2 ) = DNM1 + Z( J4P2 ) |
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Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) |
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DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU |
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DMIN = MIN( DMIN, DN ) |
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* |
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ELSE |
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* |
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* Code for non IEEE arithmetic. |
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* |
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IF( PP.EQ.0 ) THEN |
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DO 70 J4 = 4*I0, 4*( N0-3 ), 4 |
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Z( J4-2 ) = D + Z( J4-1 ) |
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IF( D.LT.ZERO ) THEN |
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RETURN |
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ELSE |
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Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) ) |
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D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU |
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END IF |
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IF( D.LT.DTHRESH) D = ZERO |
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DMIN = MIN( DMIN, D ) |
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EMIN = MIN( EMIN, Z( J4 ) ) |
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70 CONTINUE |
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ELSE |
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DO 80 J4 = 4*I0, 4*( N0-3 ), 4 |
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Z( J4-3 ) = D + Z( J4 ) |
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IF( D.LT.ZERO ) THEN |
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RETURN |
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ELSE |
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Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) ) |
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D = Z( J4+2 )*( D / Z( J4-3 ) ) - TAU |
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END IF |
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IF( D.LT.DTHRESH) D = ZERO |
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DMIN = MIN( DMIN, D ) |
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EMIN = MIN( EMIN, Z( J4-1 ) ) |
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80 CONTINUE |
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END IF |
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* |
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* Unroll last two steps. |
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* |
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DNM2 = D |
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DMIN2 = DMIN |
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J4 = 4*( N0-2 ) - PP |
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J4P2 = J4 + 2*PP - 1 |
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Z( J4-2 ) = DNM2 + Z( J4P2 ) |
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IF( DNM2.LT.ZERO ) THEN |
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RETURN |
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ELSE |
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Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) |
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DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU |
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END IF |
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DMIN = MIN( DMIN, DNM1 ) |
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* |
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DMIN1 = DMIN |
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J4 = J4 + 4 |
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J4P2 = J4 + 2*PP - 1 |
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Z( J4-2 ) = DNM1 + Z( J4P2 ) |
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IF( DNM1.LT.ZERO ) THEN |
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RETURN |
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ELSE |
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Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) |
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DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU |
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END IF |
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DMIN = MIN( DMIN, DN ) |
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* |
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END IF |
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END IF |
* |
* |
Z( J4+2 ) = DN |
Z( J4+2 ) = DN |
Z( 4*N0-PP ) = EMIN |
Z( 4*N0-PP ) = EMIN |