*> \brief \b SLASQ6 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 SLASQ6 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, * DNM1, DNM2 ) * * .. Scalar Arguments .. * INTEGER I0, N0, PP * REAL DMIN, DMIN1, DMIN2, DN, DNM1, DNM2 * .. * .. Array Arguments .. * REAL Z( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SLASQ6 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 REAL 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 REAL *> Minimum value of d. *> \endverbatim *> *> \param[out] DMIN1 *> \verbatim *> DMIN1 is REAL *> Minimum value of d, excluding D( N0 ). *> \endverbatim *> *> \param[out] DMIN2 *> \verbatim *> DMIN2 is REAL *> Minimum value of d, excluding D( N0 ) and D( N0-1 ). *> \endverbatim *> *> \param[out] DN *> \verbatim *> DN is REAL *> d(N0), the last value of d. *> \endverbatim *> *> \param[out] DNM1 *> \verbatim *> DNM1 is REAL *> d(N0-1). *> \endverbatim *> *> \param[out] DNM2 *> \verbatim *> DNM2 is REAL *> d(N0-2). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup auxOTHERcomputational * * ===================================================================== SUBROUTINE SLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, $ DNM1, DNM2 ) * * -- 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 .. INTEGER I0, N0, PP REAL DMIN, DMIN1, DMIN2, DN, DNM1, DNM2 * .. * .. Array Arguments .. REAL Z( * ) * .. * * ===================================================================== * * .. Parameter .. REAL ZERO PARAMETER ( ZERO = 0.0E0 ) * .. * .. Local Scalars .. INTEGER J4, J4P2 REAL D, EMIN, SAFMIN, TEMP * .. * .. External Function .. REAL SLAMCH EXTERNAL SLAMCH * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * IF( ( N0-I0-1 ).LE.0 ) $ RETURN * SAFMIN = SLAMCH( '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 SLASQ6 * END