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398 lines
15 KiB
398 lines
15 KiB
*> \brief \b SGET34
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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 SGET34( RMAX, LMAX, NINFO, KNT )
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*
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* .. Scalar Arguments ..
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* INTEGER KNT, LMAX
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* REAL RMAX
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* ..
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* .. Array Arguments ..
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* INTEGER NINFO( 2 )
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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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*> SGET34 tests SLAEXC, a routine for swapping adjacent blocks (either
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*> 1 by 1 or 2 by 2) on the diagonal of a matrix in real Schur form.
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*> Thus, SLAEXC computes an orthogonal matrix Q such that
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*>
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*> Q' * [ A B ] * Q = [ C1 B1 ]
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*> [ 0 C ] [ 0 A1 ]
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*>
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*> where C1 is similar to C and A1 is similar to A. Both A and C are
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*> assumed to be in standard form (equal diagonal entries and
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*> offdiagonal with differing signs) and A1 and C1 are returned with the
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*> same properties.
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*>
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*> The test code verifies these last last assertions, as well as that
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*> the residual in the above equation is small.
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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 REAL
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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 array, dimension (2)
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*> NINFO(J) is the number of examples where INFO=J occurred.
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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 single_eig
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*
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* =====================================================================
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SUBROUTINE SGET34( 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
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REAL RMAX
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* ..
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* .. Array Arguments ..
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INTEGER NINFO( 2 )
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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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REAL ZERO, HALF, ONE
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PARAMETER ( ZERO = 0.0E0, HALF = 0.5E0, ONE = 1.0E0 )
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REAL TWO, THREE
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PARAMETER ( TWO = 2.0E0, THREE = 3.0E0 )
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INTEGER LWORK
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PARAMETER ( LWORK = 32 )
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* ..
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* .. Local Scalars ..
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INTEGER I, IA, IA11, IA12, IA21, IA22, IAM, IB, IC,
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$ IC11, IC12, IC21, IC22, ICM, INFO, J
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REAL BIGNUM, EPS, RES, SMLNUM, TNRM
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* ..
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* .. Local Arrays ..
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REAL Q( 4, 4 ), RESULT( 2 ), T( 4, 4 ), T1( 4, 4 ),
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$ VAL( 9 ), VM( 2 ), WORK( LWORK )
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* ..
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* .. External Functions ..
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REAL SLAMCH
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EXTERNAL SLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL SCOPY, SLAEXC
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, REAL, SIGN, SQRT
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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 = SLAMCH( 'P' )
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SMLNUM = SLAMCH( '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 ) = ZERO
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VAL( 2 ) = SQRT( SMLNUM )
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VAL( 3 ) = ONE
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VAL( 4 ) = TWO
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VAL( 5 ) = SQRT( BIGNUM )
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VAL( 6 ) = -SQRT( SMLNUM )
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VAL( 7 ) = -ONE
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VAL( 8 ) = -TWO
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VAL( 9 ) = -SQRT( BIGNUM )
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VM( 1 ) = ONE
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VM( 2 ) = ONE + TWO*EPS
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CALL SCOPY( 16, VAL( 4 ), 0, T( 1, 1 ), 1 )
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*
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NINFO( 1 ) = 0
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NINFO( 2 ) = 0
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KNT = 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 40 IA = 1, 9
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DO 30 IAM = 1, 2
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DO 20 IB = 1, 9
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DO 10 IC = 1, 9
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T( 1, 1 ) = VAL( IA )*VM( IAM )
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T( 2, 2 ) = VAL( IC )
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T( 1, 2 ) = VAL( IB )
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T( 2, 1 ) = ZERO
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TNRM = MAX( ABS( T( 1, 1 ) ), ABS( T( 2, 2 ) ),
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$ ABS( T( 1, 2 ) ) )
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CALL SCOPY( 16, T, 1, T1, 1 )
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CALL SCOPY( 16, VAL( 1 ), 0, Q, 1 )
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CALL SCOPY( 4, VAL( 3 ), 0, Q, 5 )
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CALL SLAEXC( .TRUE., 2, T, 4, Q, 4, 1, 1, 1, WORK,
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$ INFO )
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IF( INFO.NE.0 )
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$ NINFO( INFO ) = NINFO( INFO ) + 1
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CALL SHST01( 2, 1, 2, T1, 4, T, 4, Q, 4, WORK, LWORK,
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$ RESULT )
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RES = RESULT( 1 ) + RESULT( 2 )
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IF( INFO.NE.0 )
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$ RES = RES + ONE / EPS
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IF( T( 1, 1 ).NE.T1( 2, 2 ) )
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$ RES = RES + ONE / EPS
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IF( T( 2, 2 ).NE.T1( 1, 1 ) )
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$ RES = RES + ONE / EPS
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IF( T( 2, 1 ).NE.ZERO )
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$ RES = RES + ONE / EPS
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KNT = KNT + 1
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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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40 CONTINUE
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*
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DO 110 IA = 1, 5
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DO 100 IAM = 1, 2
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DO 90 IB = 1, 5
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DO 80 IC11 = 1, 5
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DO 70 IC12 = 2, 5
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DO 60 IC21 = 2, 4
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DO 50 IC22 = -1, 1, 2
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T( 1, 1 ) = VAL( IA )*VM( IAM )
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T( 1, 2 ) = VAL( IB )
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T( 1, 3 ) = -TWO*VAL( IB )
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T( 2, 1 ) = ZERO
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T( 2, 2 ) = VAL( IC11 )
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T( 2, 3 ) = VAL( IC12 )
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T( 3, 1 ) = ZERO
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T( 3, 2 ) = -VAL( IC21 )
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T( 3, 3 ) = VAL( IC11 )*REAL( IC22 )
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TNRM = MAX( ABS( T( 1, 1 ) ),
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$ ABS( T( 1, 2 ) ), ABS( T( 1, 3 ) ),
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$ ABS( T( 2, 2 ) ), ABS( T( 2, 3 ) ),
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$ ABS( T( 3, 2 ) ), ABS( T( 3, 3 ) ) )
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CALL SCOPY( 16, T, 1, T1, 1 )
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CALL SCOPY( 16, VAL( 1 ), 0, Q, 1 )
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CALL SCOPY( 4, VAL( 3 ), 0, Q, 5 )
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CALL SLAEXC( .TRUE., 3, T, 4, Q, 4, 1, 1, 2,
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$ WORK, INFO )
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IF( INFO.NE.0 )
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$ NINFO( INFO ) = NINFO( INFO ) + 1
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CALL SHST01( 3, 1, 3, T1, 4, T, 4, Q, 4,
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$ WORK, LWORK, RESULT )
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RES = RESULT( 1 ) + RESULT( 2 )
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IF( INFO.EQ.0 ) THEN
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IF( T1( 1, 1 ).NE.T( 3, 3 ) )
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$ RES = RES + ONE / EPS
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IF( T( 3, 1 ).NE.ZERO )
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$ RES = RES + ONE / EPS
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IF( T( 3, 2 ).NE.ZERO )
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$ RES = RES + ONE / EPS
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IF( T( 2, 1 ).NE.0 .AND.
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$ ( T( 1, 1 ).NE.T( 2,
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$ 2 ) .OR. SIGN( ONE, T( 1,
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$ 2 ) ).EQ.SIGN( ONE, T( 2, 1 ) ) ) )
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$ RES = RES + ONE / EPS
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END IF
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KNT = KNT + 1
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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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50 CONTINUE
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60 CONTINUE
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70 CONTINUE
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80 CONTINUE
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90 CONTINUE
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100 CONTINUE
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110 CONTINUE
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*
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DO 180 IA11 = 1, 5
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DO 170 IA12 = 2, 5
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DO 160 IA21 = 2, 4
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DO 150 IA22 = -1, 1, 2
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DO 140 ICM = 1, 2
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DO 130 IB = 1, 5
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DO 120 IC = 1, 5
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T( 1, 1 ) = VAL( IA11 )
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T( 1, 2 ) = VAL( IA12 )
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T( 1, 3 ) = -TWO*VAL( IB )
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T( 2, 1 ) = -VAL( IA21 )
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T( 2, 2 ) = VAL( IA11 )*REAL( IA22 )
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T( 2, 3 ) = VAL( IB )
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T( 3, 1 ) = ZERO
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T( 3, 2 ) = ZERO
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T( 3, 3 ) = VAL( IC )*VM( ICM )
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TNRM = MAX( ABS( T( 1, 1 ) ),
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$ ABS( T( 1, 2 ) ), ABS( T( 1, 3 ) ),
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$ ABS( T( 2, 2 ) ), ABS( T( 2, 3 ) ),
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$ ABS( T( 3, 2 ) ), ABS( T( 3, 3 ) ) )
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CALL SCOPY( 16, T, 1, T1, 1 )
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CALL SCOPY( 16, VAL( 1 ), 0, Q, 1 )
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CALL SCOPY( 4, VAL( 3 ), 0, Q, 5 )
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CALL SLAEXC( .TRUE., 3, T, 4, Q, 4, 1, 2, 1,
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$ WORK, INFO )
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IF( INFO.NE.0 )
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$ NINFO( INFO ) = NINFO( INFO ) + 1
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CALL SHST01( 3, 1, 3, T1, 4, T, 4, Q, 4,
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$ WORK, LWORK, RESULT )
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RES = RESULT( 1 ) + RESULT( 2 )
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IF( INFO.EQ.0 ) THEN
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IF( T1( 3, 3 ).NE.T( 1, 1 ) )
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$ RES = RES + ONE / EPS
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IF( T( 2, 1 ).NE.ZERO )
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$ RES = RES + ONE / EPS
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IF( T( 3, 1 ).NE.ZERO )
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$ RES = RES + ONE / EPS
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IF( T( 3, 2 ).NE.0 .AND.
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$ ( T( 2, 2 ).NE.T( 3,
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$ 3 ) .OR. SIGN( ONE, T( 2,
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$ 3 ) ).EQ.SIGN( ONE, T( 3, 2 ) ) ) )
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$ RES = RES + ONE / EPS
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END IF
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KNT = KNT + 1
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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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120 CONTINUE
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130 CONTINUE
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140 CONTINUE
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150 CONTINUE
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160 CONTINUE
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170 CONTINUE
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180 CONTINUE
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*
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DO 300 IA11 = 1, 5
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DO 290 IA12 = 2, 5
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DO 280 IA21 = 2, 4
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DO 270 IA22 = -1, 1, 2
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DO 260 IB = 1, 5
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DO 250 IC11 = 3, 4
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DO 240 IC12 = 3, 4
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DO 230 IC21 = 3, 4
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DO 220 IC22 = -1, 1, 2
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DO 210 ICM = 5, 7
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IAM = 1
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T( 1, 1 ) = VAL( IA11 )*VM( IAM )
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T( 1, 2 ) = VAL( IA12 )*VM( IAM )
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T( 1, 3 ) = -TWO*VAL( IB )
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T( 1, 4 ) = HALF*VAL( IB )
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T( 2, 1 ) = -T( 1, 2 )*VAL( IA21 )
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T( 2, 2 ) = VAL( IA11 )*
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$ REAL( IA22 )*VM( IAM )
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T( 2, 3 ) = VAL( IB )
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T( 2, 4 ) = THREE*VAL( IB )
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T( 3, 1 ) = ZERO
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T( 3, 2 ) = ZERO
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T( 3, 3 ) = VAL( IC11 )*
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$ ABS( VAL( ICM ) )
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T( 3, 4 ) = VAL( IC12 )*
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$ ABS( VAL( ICM ) )
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T( 4, 1 ) = ZERO
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T( 4, 2 ) = ZERO
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T( 4, 3 ) = -T( 3, 4 )*VAL( IC21 )*
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$ ABS( VAL( ICM ) )
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T( 4, 4 ) = VAL( IC11 )*
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$ REAL( IC22 )*
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$ ABS( VAL( ICM ) )
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TNRM = ZERO
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DO 200 I = 1, 4
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DO 190 J = 1, 4
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TNRM = MAX( TNRM,
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$ ABS( T( I, J ) ) )
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190 CONTINUE
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200 CONTINUE
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CALL SCOPY( 16, T, 1, T1, 1 )
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CALL SCOPY( 16, VAL( 1 ), 0, Q, 1 )
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CALL SCOPY( 4, VAL( 3 ), 0, Q, 5 )
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CALL SLAEXC( .TRUE., 4, T, 4, Q, 4,
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$ 1, 2, 2, WORK, INFO )
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IF( INFO.NE.0 )
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$ NINFO( INFO ) = NINFO( INFO ) + 1
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CALL SHST01( 4, 1, 4, T1, 4, T, 4,
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$ Q, 4, WORK, LWORK,
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$ RESULT )
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RES = RESULT( 1 ) + RESULT( 2 )
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IF( INFO.EQ.0 ) THEN
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IF( T( 3, 1 ).NE.ZERO )
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$ RES = RES + ONE / EPS
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IF( T( 4, 1 ).NE.ZERO )
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$ RES = RES + ONE / EPS
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IF( T( 3, 2 ).NE.ZERO )
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$ RES = RES + ONE / EPS
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IF( T( 4, 2 ).NE.ZERO )
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$ RES = RES + ONE / EPS
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IF( T( 2, 1 ).NE.0 .AND.
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$ ( T( 1, 1 ).NE.T( 2,
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$ 2 ) .OR. SIGN( ONE, T( 1,
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$ 2 ) ).EQ.SIGN( ONE, T( 2,
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$ 1 ) ) ) )RES = RES +
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$ ONE / EPS
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IF( T( 4, 3 ).NE.0 .AND.
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$ ( T( 3, 3 ).NE.T( 4,
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$ 4 ) .OR. SIGN( ONE, T( 3,
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$ 4 ) ).EQ.SIGN( ONE, T( 4,
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$ 3 ) ) ) )RES = RES +
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$ ONE / EPS
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END IF
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KNT = KNT + 1
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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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210 CONTINUE
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220 CONTINUE
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230 CONTINUE
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240 CONTINUE
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250 CONTINUE
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260 CONTINUE
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270 CONTINUE
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280 CONTINUE
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290 CONTINUE
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300 CONTINUE
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*
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RETURN
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*
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* End of SGET34
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*
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END
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