*> \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 *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \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