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dlasq5.f
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*> \brief \b DLASQ5 computes one dqds 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 DLASQ5 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq5.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq5.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq5.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, DN,
* DNM1, DNM2, IEEE, EPS )
*
* .. Scalar Arguments ..
* LOGICAL IEEE
* INTEGER I0, N0, PP
* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU, SIGMA, EPS
* ..
* .. Array Arguments ..
* DOUBLE PRECISION Z( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLASQ5 computes one dqds transform in ping-pong form, one
*> version for IEEE machines another for non IEEE machines.
*> \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[in] TAU
*> \verbatim
*> TAU is DOUBLE PRECISION
*> This is the shift.
*> \endverbatim
*>
*> \param[in] SIGMA
*> \verbatim
*> SIGMA is DOUBLE PRECISION
*> This is the accumulated shift up to this step.
*> \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
*>
*> \param[in] IEEE
*> \verbatim
*> IEEE is LOGICAL
*> Flag for IEEE or non IEEE arithmetic.
*> \endverbatim
*>
*> \param[in] EPS
*> \verbatim
*> EPS is DOUBLE PRECISION
*> This is the value of epsilon used.
*> \endverbatim
*>
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup auxOTHERcomputational
*
* =====================================================================
SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2,
$ DN, DNM1, DNM2, IEEE, EPS )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
LOGICAL IEEE
INTEGER I0, N0, PP
DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU,
$ SIGMA, EPS
* ..
* .. Array Arguments ..
DOUBLE PRECISION Z( * )
* ..
*
* =====================================================================
*
* .. Parameter ..
DOUBLE PRECISION ZERO, HALF
PARAMETER ( ZERO = 0.0D0, HALF = 0.5 )
* ..
* .. Local Scalars ..
INTEGER J4, J4P2
DOUBLE PRECISION D, EMIN, TEMP, DTHRESH
* ..
* .. Intrinsic Functions ..
INTRINSIC MIN
* ..
* .. Executable Statements ..
*
IF( ( N0-I0-1 ).LE.0 )
$ RETURN
*
DTHRESH = EPS*(SIGMA+TAU)
IF( TAU.LT.DTHRESH*HALF ) TAU = ZERO
IF( TAU.NE.ZERO ) THEN
J4 = 4*I0 + PP - 3
EMIN = Z( J4+4 )
D = Z( J4 ) - TAU
DMIN = D
DMIN1 = -Z( J4 )
*
IF( IEEE ) THEN
*
* Code for IEEE arithmetic.
*
IF( PP.EQ.0 ) THEN
DO 10 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-2 ) = D + Z( J4-1 )
TEMP = Z( J4+1 ) / Z( J4-2 )
D = D*TEMP - TAU
DMIN = MIN( DMIN, D )
Z( J4 ) = Z( J4-1 )*TEMP
EMIN = MIN( Z( J4 ), EMIN )
10 CONTINUE
ELSE
DO 20 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-3 ) = D + Z( J4 )
TEMP = Z( J4+2 ) / Z( J4-3 )
D = D*TEMP - TAU
DMIN = MIN( DMIN, D )
Z( J4-1 ) = Z( J4 )*TEMP
EMIN = MIN( Z( J4-1 ), EMIN )
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 )
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
DMIN = MIN( DMIN, DNM1 )
*
DMIN1 = DMIN
J4 = J4 + 4
J4P2 = J4 + 2*PP - 1
Z( J4-2 ) = DNM1 + Z( J4P2 )
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
DMIN = MIN( DMIN, DN )
*
ELSE
*
* Code for non IEEE arithmetic.
*
IF( PP.EQ.0 ) THEN
DO 30 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-2 ) = D + Z( J4-1 )
IF( D.LT.ZERO ) THEN
RETURN
ELSE
Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) )
D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU
END IF
DMIN = MIN( DMIN, D )
EMIN = MIN( EMIN, Z( J4 ) )
30 CONTINUE
ELSE
DO 40 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
DMIN = MIN( DMIN, D )
EMIN = MIN( EMIN, Z( J4-1 ) )
40 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
ELSE
* This is the version that sets d's to zero if they are small enough
J4 = 4*I0 + PP - 3
EMIN = Z( J4+4 )
D = Z( J4 ) - TAU
DMIN = D
DMIN1 = -Z( J4 )
IF( IEEE ) THEN
*
* Code for IEEE arithmetic.
*
IF( PP.EQ.0 ) THEN
DO 50 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-2 ) = D + Z( J4-1 )
TEMP = Z( J4+1 ) / Z( J4-2 )
D = D*TEMP - TAU
IF( D.LT.DTHRESH ) D = ZERO
DMIN = MIN( DMIN, D )
Z( J4 ) = Z( J4-1 )*TEMP
EMIN = MIN( Z( J4 ), EMIN )
50 CONTINUE
ELSE
DO 60 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-3 ) = D + Z( J4 )
TEMP = Z( J4+2 ) / Z( J4-3 )
D = D*TEMP - TAU
IF( D.LT.DTHRESH ) D = ZERO
DMIN = MIN( DMIN, D )
Z( J4-1 ) = Z( J4 )*TEMP
EMIN = MIN( Z( J4-1 ), EMIN )
60 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 )
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
DMIN = MIN( DMIN, DNM1 )
*
DMIN1 = DMIN
J4 = J4 + 4
J4P2 = J4 + 2*PP - 1
Z( J4-2 ) = DNM1 + Z( J4P2 )
Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
DMIN = MIN( DMIN, DN )
*
ELSE
*
* Code for non IEEE arithmetic.
*
IF( PP.EQ.0 ) THEN
DO 70 J4 = 4*I0, 4*( N0-3 ), 4
Z( J4-2 ) = D + Z( J4-1 )
IF( D.LT.ZERO ) THEN
RETURN
ELSE
Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) )
D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU
END IF
IF( D.LT.DTHRESH) D = ZERO
DMIN = MIN( DMIN, D )
EMIN = MIN( EMIN, Z( J4 ) )
70 CONTINUE
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 DLASQ5
*
END