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409 lines
11 KiB
409 lines
11 KiB
2 years ago
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*> \brief <b> SLASQ5 computes one dqds transform in ping-pong form. Used by sbdsqr and sstegr. </b>
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download SLASQ5 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasq5.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/slasq5.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/slasq5.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 SLASQ5( 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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* REAL EPS, DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, SIGMA, TAU
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* ..
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* .. Array Arguments ..
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* REAL 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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*> SLASQ5 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 REAL 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 REAL
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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 REAL
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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 REAL
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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 REAL
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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 REAL
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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 REAL
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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 REAL
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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 REAL
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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 REAL
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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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*> \ingroup auxOTHERcomputational
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*
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* =====================================================================
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SUBROUTINE SLASQ5( 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 --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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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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REAL DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU,
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$ SIGMA, EPS
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* ..
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* .. Array Arguments ..
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REAL Z( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameter ..
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REAL ZERO, HALF
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PARAMETER ( ZERO = 0.0E0, HALF = 0.5 )
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* ..
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* .. Local Scalars ..
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INTEGER J4, J4P2
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REAL D, EMIN, TEMP, DTHRESH
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MIN
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* ..
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* .. Executable Statements ..
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*
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IF( ( N0-I0-1 ).LE.0 )
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$ RETURN
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*
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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
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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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*
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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 10 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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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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10 CONTINUE
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ELSE
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DO 20 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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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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20 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 30 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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DMIN = MIN( DMIN, D )
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EMIN = MIN( EMIN, Z( J4 ) )
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30 CONTINUE
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ELSE
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DO 40 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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DMIN = MIN( DMIN, D )
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EMIN = MIN( EMIN, Z( J4-1 ) )
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40 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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*
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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
|
||
|
|
DO 80 J4 = 4*I0, 4*( N0-3 ), 4
|
||
|
|
Z( J4-3 ) = D + Z( J4 )
|
||
|
|
IF( D.LT.ZERO ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) )
|
||
|
|
D = Z( J4+2 )*( D / Z( J4-3 ) ) - TAU
|
||
|
|
END IF
|
||
|
|
IF( D.LT.DTHRESH ) D = ZERO
|
||
|
|
DMIN = MIN( DMIN, D )
|
||
|
|
EMIN = MIN( EMIN, Z( J4-1 ) )
|
||
|
|
80 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Unroll last two steps.
|
||
|
|
*
|
||
|
|
DNM2 = D
|
||
|
|
DMIN2 = DMIN
|
||
|
|
J4 = 4*( N0-2 ) - PP
|
||
|
|
J4P2 = J4 + 2*PP - 1
|
||
|
|
Z( J4-2 ) = DNM2 + Z( J4P2 )
|
||
|
|
IF( DNM2.LT.ZERO ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
|
||
|
|
DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
|
||
|
|
END IF
|
||
|
|
DMIN = MIN( DMIN, DNM1 )
|
||
|
|
*
|
||
|
|
DMIN1 = DMIN
|
||
|
|
J4 = J4 + 4
|
||
|
|
J4P2 = J4 + 2*PP - 1
|
||
|
|
Z( J4-2 ) = DNM1 + Z( J4P2 )
|
||
|
|
IF( DNM1.LT.ZERO ) THEN
|
||
|
|
RETURN
|
||
|
|
ELSE
|
||
|
|
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
|
||
|
|
DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
|
||
|
|
END IF
|
||
|
|
DMIN = MIN( DMIN, DN )
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
Z( J4+2 ) = DN
|
||
|
|
Z( 4*N0-PP ) = EMIN
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of SLASQ5
|
||
|
|
*
|
||
|
|
END
|