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*> \brief \b DLASQ6 computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLASQ6 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq6.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq6.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq6.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN,
* DNM1, DNM2 )
*
* .. Scalar Arguments ..
* INTEGER I0, N0, PP
* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2
* ..
* .. Array Arguments ..
* DOUBLE PRECISION Z( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLASQ6 computes one dqd (shift equal to zero) transform in
*> ping-pong form, with protection against underflow and overflow.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] I0
*> \verbatim
*> I0 is INTEGER
*> First index.
*> \endverbatim
*>
*> \param[in] N0
*> \verbatim
*> N0 is INTEGER
*> Last index.
*> \endverbatim
*>
*> \param[in] Z
*> \verbatim
*> Z is DOUBLE PRECISION array, dimension ( 4*N )
*> Z holds the qd array. EMIN is stored in Z(4*N0) to avoid
*> an extra argument.
*> \endverbatim
*>
*> \param[in] PP
*> \verbatim
*> PP is INTEGER
*> PP=0 for ping, PP=1 for pong.
*> \endverbatim
*>
*> \param[out] DMIN
*> \verbatim
*> DMIN is DOUBLE PRECISION
*> Minimum value of d.
*> \endverbatim
*>
*> \param[out] DMIN1
*> \verbatim
*> DMIN1 is DOUBLE PRECISION
*> Minimum value of d, excluding D( N0 ).
*> \endverbatim
*>
*> \param[out] DMIN2
*> \verbatim
*> DMIN2 is DOUBLE PRECISION
*> Minimum value of d, excluding D( N0 ) and D( N0-1 ).
*> \endverbatim
*>
*> \param[out] DN
*> \verbatim
*> DN is DOUBLE PRECISION
*> d(N0), the last value of d.
*> \endverbatim
*>
*> \param[out] DNM1
*> \verbatim
*> DNM1 is DOUBLE PRECISION
*> d(N0-1).
*> \endverbatim
*>
*> \param[out] DNM2
*> \verbatim
*> DNM2 is DOUBLE PRECISION
*> d(N0-2).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup auxOTHERcomputational
*
* =====================================================================
SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN,
$ DNM1, DNM2 )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER I0, N0, PP
DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2
* ..
* .. Array Arguments ..
DOUBLE PRECISION Z( * )
* ..
*
* =====================================================================
*
* .. Parameter ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
* ..
* .. Local Scalars ..
INTEGER J4, J4P2
DOUBLE PRECISION D, EMIN, SAFMIN, TEMP
* ..
* .. External Function ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC MIN
* ..
* .. Executable Statements ..
*
IF( ( N0-I0-1 ).LE.0 )
$ RETURN
*
SAFMIN = DLAMCH( 'Safe minimum' )
J4 = 4*I0 + PP - 3
EMIN = Z( J4+4 )
D = Z( J4 )
DMIN = D
*
IF( PP.EQ.0 ) THEN
DO 10 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-2 ) = D + Z( J4-1 )
IF( Z( J4-2 ).EQ.ZERO ) THEN
Z( J4 ) = ZERO
D = Z( J4+1 )
DMIN = D
EMIN = ZERO
ELSE IF( SAFMIN*Z( J4+1 ).LT.Z( J4-2 ) .AND.
$ SAFMIN*Z( J4-2 ).LT.Z( J4+1 ) ) THEN
TEMP = Z( J4+1 ) / Z( J4-2 )
Z( J4 ) = Z( J4-1 )*TEMP
D = D*TEMP
ELSE
Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) )
D = Z( J4+1 )*( D / Z( J4-2 ) )
END IF
DMIN = MIN( DMIN, D )
EMIN = MIN( EMIN, Z( J4 ) )
10 CONTINUE
ELSE
DO 20 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-3 ) = D + Z( J4 )
IF( Z( J4-3 ).EQ.ZERO ) THEN
Z( J4-1 ) = ZERO
D = Z( J4+2 )
DMIN = D
EMIN = ZERO
ELSE IF( SAFMIN*Z( J4+2 ).LT.Z( J4-3 ) .AND.
$ SAFMIN*Z( J4-3 ).LT.Z( J4+2 ) ) THEN
TEMP = Z( J4+2 ) / Z( J4-3 )
Z( J4-1 ) = Z( J4 )*TEMP
D = D*TEMP
ELSE
Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) )
D = Z( J4+2 )*( D / Z( J4-3 ) )
END IF
DMIN = MIN( DMIN, D )
EMIN = MIN( EMIN, Z( J4-1 ) )
20 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( Z( J4-2 ).EQ.ZERO ) THEN
Z( J4 ) = ZERO
DNM1 = Z( J4P2+2 )
DMIN = DNM1
EMIN = ZERO
ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND.
$ SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN
TEMP = Z( J4P2+2 ) / Z( J4-2 )
Z( J4 ) = Z( J4P2 )*TEMP
DNM1 = DNM2*TEMP
ELSE
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) )
END IF
DMIN = MIN( DMIN, DNM1 )
*
DMIN1 = DMIN
J4 = J4 + 4
J4P2 = J4 + 2*PP - 1
Z( J4-2 ) = DNM1 + Z( J4P2 )
IF( Z( J4-2 ).EQ.ZERO ) THEN
Z( J4 ) = ZERO
DN = Z( J4P2+2 )
DMIN = DN
EMIN = ZERO
ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND.
$ SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN
TEMP = Z( J4P2+2 ) / Z( J4-2 )
Z( J4 ) = Z( J4P2 )*TEMP
DN = DNM1*TEMP
ELSE
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) )
END IF
DMIN = MIN( DMIN, DN )
*
Z( J4+2 ) = DN
Z( 4*N0-PP ) = EMIN
RETURN
*
* End of DLASQ6
*
END
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