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428 lines
18 KiB
428 lines
18 KiB
2 years ago
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*> \brief \b DGET32
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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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* Definition:
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* ===========
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*
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* SUBROUTINE DGET32( RMAX, LMAX, NINFO, KNT )
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*
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* .. Scalar Arguments ..
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* INTEGER KNT, LMAX, NINFO
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* DOUBLE PRECISION RMAX
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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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*> DGET32 tests DLASY2, a routine for solving
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*>
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*> op(TL)*X + ISGN*X*op(TR) = SCALE*B
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*>
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*> where TL is N1 by N1, TR is N2 by N2, and N1,N2 =1 or 2 only.
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*> X and B are N1 by N2, op() is an optional transpose, an
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*> ISGN = 1 or -1. SCALE is chosen less than or equal to 1 to
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*> avoid overflow in X.
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*>
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*> The test condition is that the scaled residual
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*>
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*> norm( op(TL)*X + ISGN*X*op(TR) = SCALE*B )
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*> / ( max( ulp*norm(TL), ulp*norm(TR)) * norm(X), SMLNUM )
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*>
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*> should be on the order of 1. Here, ulp is the machine precision.
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*> Also, it is verified that SCALE is less than or equal to 1, and
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*> that XNORM = infinity-norm(X).
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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[out] RMAX
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*> \verbatim
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*> RMAX is DOUBLE PRECISION
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*> Value of the largest test ratio.
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*> \endverbatim
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*>
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*> \param[out] LMAX
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*> \verbatim
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*> LMAX is INTEGER
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*> Example number where largest test ratio achieved.
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*> \endverbatim
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*>
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*> \param[out] NINFO
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*> \verbatim
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*> NINFO is INTEGER
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*> Number of examples returned with INFO.NE.0.
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*> \endverbatim
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*>
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*> \param[out] KNT
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*> \verbatim
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*> KNT is INTEGER
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*> Total number of examples tested.
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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 double_eig
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*
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* =====================================================================
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SUBROUTINE DGET32( RMAX, LMAX, NINFO, KNT )
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*
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* -- LAPACK test 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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INTEGER KNT, LMAX, NINFO
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DOUBLE PRECISION RMAX
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
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DOUBLE PRECISION TWO, FOUR, EIGHT
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PARAMETER ( TWO = 2.0D0, FOUR = 4.0D0, EIGHT = 8.0D0 )
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* ..
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* .. Local Scalars ..
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LOGICAL LTRANL, LTRANR
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INTEGER IB, IB1, IB2, IB3, INFO, ISGN, ITL, ITLSCL,
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$ ITR, ITRANL, ITRANR, ITRSCL, N1, N2
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DOUBLE PRECISION BIGNUM, DEN, EPS, RES, SCALE, SGN, SMLNUM, TMP,
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$ TNRM, XNORM, XNRM
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* ..
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* .. Local Arrays ..
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INTEGER ITVAL( 2, 2, 8 )
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DOUBLE PRECISION B( 2, 2 ), TL( 2, 2 ), TR( 2, 2 ), VAL( 3 ),
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$ X( 2, 2 )
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH
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EXTERNAL DLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL DLASY2
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, MIN, SQRT
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* ..
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* .. Data statements ..
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DATA ITVAL / 8, 4, 2, 1, 4, 8, 1, 2, 2, 1, 8, 4, 1,
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$ 2, 4, 8, 9, 4, 2, 1, 4, 9, 1, 2, 2, 1, 9, 4, 1,
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$ 2, 4, 9 /
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* ..
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* .. Executable Statements ..
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*
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* Get machine parameters
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*
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EPS = DLAMCH( 'P' )
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SMLNUM = DLAMCH( 'S' ) / EPS
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BIGNUM = ONE / SMLNUM
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*
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* Set up test case parameters
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*
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VAL( 1 ) = SQRT( SMLNUM )
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VAL( 2 ) = ONE
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VAL( 3 ) = SQRT( BIGNUM )
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*
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KNT = 0
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NINFO = 0
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LMAX = 0
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RMAX = ZERO
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*
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* Begin test loop
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*
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DO 230 ITRANL = 0, 1
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DO 220 ITRANR = 0, 1
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DO 210 ISGN = -1, 1, 2
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SGN = ISGN
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LTRANL = ITRANL.EQ.1
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LTRANR = ITRANR.EQ.1
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*
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N1 = 1
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N2 = 1
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DO 30 ITL = 1, 3
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DO 20 ITR = 1, 3
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DO 10 IB = 1, 3
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TL( 1, 1 ) = VAL( ITL )
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TR( 1, 1 ) = VAL( ITR )
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B( 1, 1 ) = VAL( IB )
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KNT = KNT + 1
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CALL DLASY2( LTRANL, LTRANR, ISGN, N1, N2, TL,
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$ 2, TR, 2, B, 2, SCALE, X, 2, XNORM,
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$ INFO )
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IF( INFO.NE.0 )
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$ NINFO = NINFO + 1
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RES = ABS( ( TL( 1, 1 )+SGN*TR( 1, 1 ) )*
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$ X( 1, 1 )-SCALE*B( 1, 1 ) )
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IF( INFO.EQ.0 ) THEN
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DEN = MAX( EPS*( ( ABS( TR( 1,
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$ 1 ) )+ABS( TL( 1, 1 ) ) )*ABS( X( 1,
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$ 1 ) ) ), SMLNUM )
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ELSE
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DEN = SMLNUM*MAX( ABS( X( 1, 1 ) ), ONE )
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END IF
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RES = RES / DEN
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IF( SCALE.GT.ONE )
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$ RES = RES + ONE / EPS
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RES = RES + ABS( XNORM-ABS( X( 1, 1 ) ) ) /
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$ MAX( SMLNUM, XNORM ) / EPS
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IF( INFO.NE.0 .AND. INFO.NE.1 )
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$ RES = RES + ONE / EPS
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IF( RES.GT.RMAX ) THEN
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LMAX = KNT
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RMAX = RES
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END IF
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10 CONTINUE
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20 CONTINUE
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30 CONTINUE
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*
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N1 = 2
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N2 = 1
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DO 80 ITL = 1, 8
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DO 70 ITLSCL = 1, 3
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DO 60 ITR = 1, 3
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DO 50 IB1 = 1, 3
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DO 40 IB2 = 1, 3
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B( 1, 1 ) = VAL( IB1 )
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B( 2, 1 ) = -FOUR*VAL( IB2 )
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TL( 1, 1 ) = ITVAL( 1, 1, ITL )*
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$ VAL( ITLSCL )
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TL( 2, 1 ) = ITVAL( 2, 1, ITL )*
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$ VAL( ITLSCL )
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TL( 1, 2 ) = ITVAL( 1, 2, ITL )*
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$ VAL( ITLSCL )
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TL( 2, 2 ) = ITVAL( 2, 2, ITL )*
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$ VAL( ITLSCL )
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TR( 1, 1 ) = VAL( ITR )
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KNT = KNT + 1
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CALL DLASY2( LTRANL, LTRANR, ISGN, N1, N2,
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$ TL, 2, TR, 2, B, 2, SCALE, X,
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$ 2, XNORM, INFO )
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IF( INFO.NE.0 )
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$ NINFO = NINFO + 1
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IF( LTRANL ) THEN
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TMP = TL( 1, 2 )
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TL( 1, 2 ) = TL( 2, 1 )
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TL( 2, 1 ) = TMP
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END IF
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RES = ABS( ( TL( 1, 1 )+SGN*TR( 1, 1 ) )*
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$ X( 1, 1 )+TL( 1, 2 )*X( 2, 1 )-
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$ SCALE*B( 1, 1 ) )
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RES = RES + ABS( ( TL( 2, 2 )+SGN*TR( 1,
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$ 1 ) )*X( 2, 1 )+TL( 2, 1 )*
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$ X( 1, 1 )-SCALE*B( 2, 1 ) )
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TNRM = ABS( TR( 1, 1 ) ) +
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$ ABS( TL( 1, 1 ) ) +
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$ ABS( TL( 1, 2 ) ) +
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$ ABS( TL( 2, 1 ) ) +
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$ ABS( TL( 2, 2 ) )
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XNRM = MAX( ABS( X( 1, 1 ) ),
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$ ABS( X( 2, 1 ) ) )
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DEN = MAX( SMLNUM, SMLNUM*XNRM,
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$ ( TNRM*EPS )*XNRM )
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RES = RES / DEN
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IF( SCALE.GT.ONE )
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$ RES = RES + ONE / EPS
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RES = RES + ABS( XNORM-XNRM ) /
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$ MAX( SMLNUM, XNORM ) / EPS
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IF( RES.GT.RMAX ) THEN
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LMAX = KNT
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RMAX = RES
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END IF
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40 CONTINUE
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50 CONTINUE
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60 CONTINUE
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70 CONTINUE
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80 CONTINUE
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*
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N1 = 1
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N2 = 2
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DO 130 ITR = 1, 8
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DO 120 ITRSCL = 1, 3
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DO 110 ITL = 1, 3
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DO 100 IB1 = 1, 3
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DO 90 IB2 = 1, 3
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B( 1, 1 ) = VAL( IB1 )
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B( 1, 2 ) = -TWO*VAL( IB2 )
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TR( 1, 1 ) = ITVAL( 1, 1, ITR )*
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$ VAL( ITRSCL )
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TR( 2, 1 ) = ITVAL( 2, 1, ITR )*
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$ VAL( ITRSCL )
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TR( 1, 2 ) = ITVAL( 1, 2, ITR )*
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$ VAL( ITRSCL )
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TR( 2, 2 ) = ITVAL( 2, 2, ITR )*
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$ VAL( ITRSCL )
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TL( 1, 1 ) = VAL( ITL )
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KNT = KNT + 1
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CALL DLASY2( LTRANL, LTRANR, ISGN, N1, N2,
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$ TL, 2, TR, 2, B, 2, SCALE, X,
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$ 2, XNORM, INFO )
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IF( INFO.NE.0 )
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$ NINFO = NINFO + 1
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IF( LTRANR ) THEN
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TMP = TR( 1, 2 )
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TR( 1, 2 ) = TR( 2, 1 )
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TR( 2, 1 ) = TMP
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END IF
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TNRM = ABS( TL( 1, 1 ) ) +
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$ ABS( TR( 1, 1 ) ) +
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$ ABS( TR( 1, 2 ) ) +
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$ ABS( TR( 2, 2 ) ) +
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$ ABS( TR( 2, 1 ) )
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XNRM = ABS( X( 1, 1 ) ) + ABS( X( 1, 2 ) )
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RES = ABS( ( ( TL( 1, 1 )+SGN*TR( 1,
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$ 1 ) ) )*( X( 1, 1 ) )+
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$ ( SGN*TR( 2, 1 ) )*( X( 1, 2 ) )-
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$ ( SCALE*B( 1, 1 ) ) )
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RES = RES + ABS( ( ( TL( 1, 1 )+SGN*TR( 2,
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$ 2 ) ) )*( X( 1, 2 ) )+
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$ ( SGN*TR( 1, 2 ) )*( X( 1, 1 ) )-
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$ ( SCALE*B( 1, 2 ) ) )
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DEN = MAX( SMLNUM, SMLNUM*XNRM,
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$ ( TNRM*EPS )*XNRM )
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RES = RES / DEN
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IF( SCALE.GT.ONE )
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$ RES = RES + ONE / EPS
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RES = RES + ABS( XNORM-XNRM ) /
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$ MAX( SMLNUM, XNORM ) / EPS
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IF( RES.GT.RMAX ) THEN
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LMAX = KNT
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RMAX = RES
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END IF
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90 CONTINUE
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100 CONTINUE
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110 CONTINUE
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120 CONTINUE
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130 CONTINUE
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*
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N1 = 2
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N2 = 2
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DO 200 ITR = 1, 8
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DO 190 ITRSCL = 1, 3
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DO 180 ITL = 1, 8
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DO 170 ITLSCL = 1, 3
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DO 160 IB1 = 1, 3
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DO 150 IB2 = 1, 3
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DO 140 IB3 = 1, 3
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B( 1, 1 ) = VAL( IB1 )
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B( 2, 1 ) = -FOUR*VAL( IB2 )
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B( 1, 2 ) = -TWO*VAL( IB3 )
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B( 2, 2 ) = EIGHT*
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$ MIN( VAL( IB1 ), VAL
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$ ( IB2 ), VAL( IB3 ) )
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TR( 1, 1 ) = ITVAL( 1, 1, ITR )*
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$ VAL( ITRSCL )
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TR( 2, 1 ) = ITVAL( 2, 1, ITR )*
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$ VAL( ITRSCL )
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TR( 1, 2 ) = ITVAL( 1, 2, ITR )*
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$ VAL( ITRSCL )
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TR( 2, 2 ) = ITVAL( 2, 2, ITR )*
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$ VAL( ITRSCL )
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TL( 1, 1 ) = ITVAL( 1, 1, ITL )*
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$ VAL( ITLSCL )
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TL( 2, 1 ) = ITVAL( 2, 1, ITL )*
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$ VAL( ITLSCL )
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TL( 1, 2 ) = ITVAL( 1, 2, ITL )*
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$ VAL( ITLSCL )
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TL( 2, 2 ) = ITVAL( 2, 2, ITL )*
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$ VAL( ITLSCL )
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KNT = KNT + 1
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CALL DLASY2( LTRANL, LTRANR, ISGN,
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$ N1, N2, TL, 2, TR, 2,
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$ B, 2, SCALE, X, 2,
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$ XNORM, INFO )
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IF( INFO.NE.0 )
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$ NINFO = NINFO + 1
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IF( LTRANR ) THEN
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TMP = TR( 1, 2 )
|
||
|
|
TR( 1, 2 ) = TR( 2, 1 )
|
||
|
|
TR( 2, 1 ) = TMP
|
||
|
|
END IF
|
||
|
|
IF( LTRANL ) THEN
|
||
|
|
TMP = TL( 1, 2 )
|
||
|
|
TL( 1, 2 ) = TL( 2, 1 )
|
||
|
|
TL( 2, 1 ) = TMP
|
||
|
|
END IF
|
||
|
|
TNRM = ABS( TR( 1, 1 ) ) +
|
||
|
|
$ ABS( TR( 2, 1 ) ) +
|
||
|
|
$ ABS( TR( 1, 2 ) ) +
|
||
|
|
$ ABS( TR( 2, 2 ) ) +
|
||
|
|
$ ABS( TL( 1, 1 ) ) +
|
||
|
|
$ ABS( TL( 2, 1 ) ) +
|
||
|
|
$ ABS( TL( 1, 2 ) ) +
|
||
|
|
$ ABS( TL( 2, 2 ) )
|
||
|
|
XNRM = MAX( ABS( X( 1, 1 ) )+
|
||
|
|
$ ABS( X( 1, 2 ) ),
|
||
|
|
$ ABS( X( 2, 1 ) )+
|
||
|
|
$ ABS( X( 2, 2 ) ) )
|
||
|
|
RES = ABS( ( ( TL( 1, 1 )+SGN*TR( 1,
|
||
|
|
$ 1 ) ) )*( X( 1, 1 ) )+
|
||
|
|
$ ( SGN*TR( 2, 1 ) )*
|
||
|
|
$ ( X( 1, 2 ) )+( TL( 1, 2 ) )*
|
||
|
|
$ ( X( 2, 1 ) )-
|
||
|
|
$ ( SCALE*B( 1, 1 ) ) )
|
||
|
|
RES = RES + ABS( ( TL( 1, 1 ) )*
|
||
|
|
$ ( X( 1, 2 ) )+
|
||
|
|
$ ( SGN*TR( 1, 2 ) )*
|
||
|
|
$ ( X( 1, 1 ) )+
|
||
|
|
$ ( SGN*TR( 2, 2 ) )*
|
||
|
|
$ ( X( 1, 2 ) )+( TL( 1, 2 ) )*
|
||
|
|
$ ( X( 2, 2 ) )-
|
||
|
|
$ ( SCALE*B( 1, 2 ) ) )
|
||
|
|
RES = RES + ABS( ( TL( 2, 1 ) )*
|
||
|
|
$ ( X( 1, 1 ) )+
|
||
|
|
$ ( SGN*TR( 1, 1 ) )*
|
||
|
|
$ ( X( 2, 1 ) )+
|
||
|
|
$ ( SGN*TR( 2, 1 ) )*
|
||
|
|
$ ( X( 2, 2 ) )+( TL( 2, 2 ) )*
|
||
|
|
$ ( X( 2, 1 ) )-
|
||
|
|
$ ( SCALE*B( 2, 1 ) ) )
|
||
|
|
RES = RES + ABS( ( ( TL( 2,
|
||
|
|
$ 2 )+SGN*TR( 2, 2 ) ) )*
|
||
|
|
$ ( X( 2, 2 ) )+
|
||
|
|
$ ( SGN*TR( 1, 2 ) )*
|
||
|
|
$ ( X( 2, 1 ) )+( TL( 2, 1 ) )*
|
||
|
|
$ ( X( 1, 2 ) )-
|
||
|
|
$ ( SCALE*B( 2, 2 ) ) )
|
||
|
|
DEN = MAX( SMLNUM, SMLNUM*XNRM,
|
||
|
|
$ ( TNRM*EPS )*XNRM )
|
||
|
|
RES = RES / DEN
|
||
|
|
IF( SCALE.GT.ONE )
|
||
|
|
$ RES = RES + ONE / EPS
|
||
|
|
RES = RES + ABS( XNORM-XNRM ) /
|
||
|
|
$ MAX( SMLNUM, XNORM ) / EPS
|
||
|
|
IF( RES.GT.RMAX ) THEN
|
||
|
|
LMAX = KNT
|
||
|
|
RMAX = RES
|
||
|
|
END IF
|
||
|
|
140 CONTINUE
|
||
|
|
150 CONTINUE
|
||
|
|
160 CONTINUE
|
||
|
|
170 CONTINUE
|
||
|
|
180 CONTINUE
|
||
|
|
190 CONTINUE
|
||
|
|
200 CONTINUE
|
||
|
|
210 CONTINUE
|
||
|
|
220 CONTINUE
|
||
|
|
230 CONTINUE
|
||
|
|
*
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of DGET32
|
||
|
|
*
|
||
|
|
END
|