519 lines
22 KiB
Fortran
519 lines
22 KiB
Fortran
*> \brief \b SGET31
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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 SGET31( 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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*> SGET31 tests SLALN2, a routine for solving
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*>
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*> (ca A - w D)X = sB
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*>
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*> where A is an NA by NA matrix (NA=1 or 2 only), w is a real (NW=1) or
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*> complex (NW=2) constant, ca is a real constant, D is an NA by NA real
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*> diagonal matrix, and B is an NA by NW matrix (when NW=2 the second
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*> column of B contains the imaginary part of the solution). The code
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*> returns X and s, where s is a scale factor, less than or equal to 1,
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*> which is chosen to avoid overflow in X.
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*>
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*> If any singular values of ca A-w D are less than another input
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*> parameter SMIN, they are perturbed up to SMIN.
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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( (ca A-w D)*X - s*B ) /
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*> ( max( ulp*norm(ca A-w D), SMIN )*norm(X) )
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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 that
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*> 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 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 (3)
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*> NINFO(1) = number of examples with INFO less than 0
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*> NINFO(2) = number of examples with INFO greater than 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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*> \date November 2011
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*
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*> \ingroup single_eig
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*
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* =====================================================================
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SUBROUTINE SGET31( RMAX, LMAX, NINFO, KNT )
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*
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* -- LAPACK test routine (version 3.4.0) --
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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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* November 2011
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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, FOUR
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PARAMETER ( TWO = 2.0E0, THREE = 3.0E0, FOUR = 4.0E0 )
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REAL SEVEN, TEN
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PARAMETER ( SEVEN = 7.0E0, TEN = 10.0E0 )
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REAL TWNONE
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PARAMETER ( TWNONE = 21.0E0 )
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* ..
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* .. Local Scalars ..
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INTEGER IA, IB, ICA, ID1, ID2, INFO, ISMIN, ITRANS,
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$ IWI, IWR, NA, NW
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REAL BIGNUM, CA, D1, D2, DEN, EPS, RES, SCALE, SMIN,
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$ SMLNUM, TMP, UNFL, WI, WR, XNORM
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* ..
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* .. Local Arrays ..
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LOGICAL LTRANS( 0: 1 )
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REAL A( 2, 2 ), B( 2, 2 ), VAB( 3 ), VCA( 5 ),
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$ VDD( 4 ), VSMIN( 4 ), VWI( 4 ), VWR( 4 ),
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$ X( 2, 2 )
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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 SLABAD, SLALN2
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, SQRT
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* ..
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* .. Data statements ..
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DATA LTRANS / .FALSE., .TRUE. /
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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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UNFL = SLAMCH( 'U' )
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SMLNUM = SLAMCH( 'S' ) / EPS
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BIGNUM = ONE / SMLNUM
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CALL SLABAD( SMLNUM, BIGNUM )
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*
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* Set up test case parameters
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*
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VSMIN( 1 ) = SMLNUM
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VSMIN( 2 ) = EPS
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VSMIN( 3 ) = ONE / ( TEN*TEN )
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VSMIN( 4 ) = ONE / EPS
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VAB( 1 ) = SQRT( SMLNUM )
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VAB( 2 ) = ONE
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VAB( 3 ) = SQRT( BIGNUM )
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VWR( 1 ) = ZERO
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VWR( 2 ) = HALF
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VWR( 3 ) = TWO
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VWR( 4 ) = ONE
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VWI( 1 ) = SMLNUM
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VWI( 2 ) = EPS
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VWI( 3 ) = ONE
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VWI( 4 ) = TWO
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VDD( 1 ) = SQRT( SMLNUM )
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VDD( 2 ) = ONE
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VDD( 3 ) = TWO
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VDD( 4 ) = SQRT( BIGNUM )
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VCA( 1 ) = ZERO
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VCA( 2 ) = SQRT( SMLNUM )
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VCA( 3 ) = EPS
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VCA( 4 ) = HALF
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VCA( 5 ) = ONE
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*
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KNT = 0
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NINFO( 1 ) = 0
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NINFO( 2 ) = 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 190 ID1 = 1, 4
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D1 = VDD( ID1 )
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DO 180 ID2 = 1, 4
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D2 = VDD( ID2 )
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DO 170 ICA = 1, 5
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CA = VCA( ICA )
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DO 160 ITRANS = 0, 1
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DO 150 ISMIN = 1, 4
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SMIN = VSMIN( ISMIN )
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*
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NA = 1
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NW = 1
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DO 30 IA = 1, 3
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A( 1, 1 ) = VAB( IA )
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DO 20 IB = 1, 3
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B( 1, 1 ) = VAB( IB )
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DO 10 IWR = 1, 4
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IF( D1.EQ.ONE .AND. D2.EQ.ONE .AND. CA.EQ.
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$ ONE ) THEN
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WR = VWR( IWR )*A( 1, 1 )
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ELSE
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WR = VWR( IWR )
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END IF
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WI = ZERO
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CALL SLALN2( LTRANS( ITRANS ), NA, NW,
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$ SMIN, CA, A, 2, D1, D2, B, 2,
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$ WR, WI, X, 2, SCALE, XNORM,
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$ INFO )
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IF( INFO.LT.0 )
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$ NINFO( 1 ) = NINFO( 1 ) + 1
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IF( INFO.GT.0 )
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$ NINFO( 2 ) = NINFO( 2 ) + 1
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RES = ABS( ( CA*A( 1, 1 )-WR*D1 )*
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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( ( CA*A( 1,
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$ 1 )-WR*D1 )*X( 1, 1 ) ) ),
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$ SMLNUM )
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ELSE
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DEN = MAX( SMIN*ABS( X( 1, 1 ) ),
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$ SMLNUM )
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END IF
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RES = RES / DEN
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IF( ABS( X( 1, 1 ) ).LT.UNFL .AND.
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$ ABS( B( 1, 1 ) ).LE.SMLNUM*
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$ ABS( CA*A( 1, 1 )-WR*D1 ) )RES = ZERO
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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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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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*
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NA = 1
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NW = 2
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DO 70 IA = 1, 3
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A( 1, 1 ) = VAB( IA )
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DO 60 IB = 1, 3
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B( 1, 1 ) = VAB( IB )
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B( 1, 2 ) = -HALF*VAB( IB )
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DO 50 IWR = 1, 4
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IF( D1.EQ.ONE .AND. D2.EQ.ONE .AND. CA.EQ.
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$ ONE ) THEN
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WR = VWR( IWR )*A( 1, 1 )
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ELSE
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WR = VWR( IWR )
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END IF
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DO 40 IWI = 1, 4
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IF( D1.EQ.ONE .AND. D2.EQ.ONE .AND.
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$ CA.EQ.ONE ) THEN
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WI = VWI( IWI )*A( 1, 1 )
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ELSE
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WI = VWI( IWI )
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END IF
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CALL SLALN2( LTRANS( ITRANS ), NA, NW,
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$ SMIN, CA, A, 2, D1, D2, B,
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$ 2, WR, WI, X, 2, SCALE,
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$ XNORM, INFO )
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IF( INFO.LT.0 )
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$ NINFO( 1 ) = NINFO( 1 ) + 1
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IF( INFO.GT.0 )
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$ NINFO( 2 ) = NINFO( 2 ) + 1
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RES = ABS( ( CA*A( 1, 1 )-WR*D1 )*
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$ X( 1, 1 )+( WI*D1 )*X( 1, 2 )-
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$ SCALE*B( 1, 1 ) )
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RES = RES + ABS( ( -WI*D1 )*X( 1, 1 )+
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$ ( CA*A( 1, 1 )-WR*D1 )*X( 1, 2 )-
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$ SCALE*B( 1, 2 ) )
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IF( INFO.EQ.0 ) THEN
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DEN = MAX( EPS*( MAX( ABS( CA*A( 1,
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$ 1 )-WR*D1 ), ABS( D1*WI ) )*
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$ ( ABS( X( 1, 1 ) )+ABS( X( 1,
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$ 2 ) ) ) ), SMLNUM )
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ELSE
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DEN = MAX( SMIN*( ABS( X( 1,
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$ 1 ) )+ABS( X( 1, 2 ) ) ),
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$ SMLNUM )
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END IF
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RES = RES / DEN
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IF( ABS( X( 1, 1 ) ).LT.UNFL .AND.
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$ ABS( X( 1, 2 ) ).LT.UNFL .AND.
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$ ABS( B( 1, 1 ) ).LE.SMLNUM*
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$ ABS( CA*A( 1, 1 )-WR*D1 ) )
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$ RES = ZERO
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IF( SCALE.GT.ONE )
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$ RES = RES + ONE / EPS
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RES = RES + ABS( XNORM-
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$ ABS( X( 1, 1 ) )-
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$ ABS( X( 1, 2 ) ) ) /
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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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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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40 CONTINUE
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50 CONTINUE
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60 CONTINUE
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70 CONTINUE
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*
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NA = 2
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NW = 1
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DO 100 IA = 1, 3
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A( 1, 1 ) = VAB( IA )
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A( 1, 2 ) = -THREE*VAB( IA )
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A( 2, 1 ) = -SEVEN*VAB( IA )
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A( 2, 2 ) = TWNONE*VAB( IA )
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DO 90 IB = 1, 3
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B( 1, 1 ) = VAB( IB )
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B( 2, 1 ) = -TWO*VAB( IB )
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DO 80 IWR = 1, 4
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IF( D1.EQ.ONE .AND. D2.EQ.ONE .AND. CA.EQ.
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$ ONE ) THEN
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WR = VWR( IWR )*A( 1, 1 )
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ELSE
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WR = VWR( IWR )
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END IF
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WI = ZERO
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CALL SLALN2( LTRANS( ITRANS ), NA, NW,
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$ SMIN, CA, A, 2, D1, D2, B, 2,
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$ WR, WI, X, 2, SCALE, XNORM,
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$ INFO )
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IF( INFO.LT.0 )
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$ NINFO( 1 ) = NINFO( 1 ) + 1
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IF( INFO.GT.0 )
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$ NINFO( 2 ) = NINFO( 2 ) + 1
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IF( ITRANS.EQ.1 ) THEN
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TMP = A( 1, 2 )
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A( 1, 2 ) = A( 2, 1 )
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A( 2, 1 ) = TMP
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END IF
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RES = ABS( ( CA*A( 1, 1 )-WR*D1 )*
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$ X( 1, 1 )+( CA*A( 1, 2 ) )*
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$ X( 2, 1 )-SCALE*B( 1, 1 ) )
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RES = RES + ABS( ( CA*A( 2, 1 ) )*
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$ X( 1, 1 )+( CA*A( 2, 2 )-WR*D2 )*
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$ X( 2, 1 )-SCALE*B( 2, 1 ) )
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IF( INFO.EQ.0 ) THEN
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DEN = MAX( EPS*( MAX( ABS( CA*A( 1,
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$ 1 )-WR*D1 )+ABS( CA*A( 1, 2 ) ),
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$ ABS( CA*A( 2, 1 ) )+ABS( CA*A( 2,
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$ 2 )-WR*D2 ) )*MAX( ABS( X( 1,
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$ 1 ) ), ABS( X( 2, 1 ) ) ) ),
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$ SMLNUM )
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ELSE
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DEN = MAX( EPS*( MAX( SMIN / EPS,
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$ MAX( ABS( CA*A( 1,
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$ 1 )-WR*D1 )+ABS( CA*A( 1, 2 ) ),
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$ ABS( CA*A( 2, 1 ) )+ABS( CA*A( 2,
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$ 2 )-WR*D2 ) ) )*MAX( ABS( X( 1,
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$ 1 ) ), ABS( X( 2, 1 ) ) ) ),
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$ SMLNUM )
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END IF
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RES = RES / DEN
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IF( ABS( X( 1, 1 ) ).LT.UNFL .AND.
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$ ABS( X( 2, 1 ) ).LT.UNFL .AND.
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$ ABS( B( 1, 1 ) )+ABS( B( 2, 1 ) ).LE.
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$ SMLNUM*( ABS( CA*A( 1,
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$ 1 )-WR*D1 )+ABS( CA*A( 1,
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$ 2 ) )+ABS( CA*A( 2,
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$ 1 ) )+ABS( CA*A( 2, 2 )-WR*D2 ) ) )
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$ RES = ZERO
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IF( SCALE.GT.ONE )
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$ RES = RES + ONE / EPS
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RES = RES + ABS( XNORM-
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$ MAX( ABS( X( 1, 1 ) ), ABS( X( 2,
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$ 1 ) ) ) ) / MAX( SMLNUM, XNORM ) /
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$ 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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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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80 CONTINUE
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90 CONTINUE
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100 CONTINUE
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*
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NA = 2
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NW = 2
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DO 140 IA = 1, 3
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A( 1, 1 ) = VAB( IA )*TWO
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A( 1, 2 ) = -THREE*VAB( IA )
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A( 2, 1 ) = -SEVEN*VAB( IA )
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A( 2, 2 ) = TWNONE*VAB( IA )
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DO 130 IB = 1, 3
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B( 1, 1 ) = VAB( IB )
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B( 2, 1 ) = -TWO*VAB( IB )
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B( 1, 2 ) = FOUR*VAB( IB )
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B( 2, 2 ) = -SEVEN*VAB( IB )
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DO 120 IWR = 1, 4
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IF( D1.EQ.ONE .AND. D2.EQ.ONE .AND. CA.EQ.
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$ ONE ) THEN
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WR = VWR( IWR )*A( 1, 1 )
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ELSE
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WR = VWR( IWR )
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END IF
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DO 110 IWI = 1, 4
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IF( D1.EQ.ONE .AND. D2.EQ.ONE .AND.
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$ CA.EQ.ONE ) THEN
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WI = VWI( IWI )*A( 1, 1 )
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ELSE
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WI = VWI( IWI )
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END IF
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CALL SLALN2( LTRANS( ITRANS ), NA, NW,
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$ SMIN, CA, A, 2, D1, D2, B,
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$ 2, WR, WI, X, 2, SCALE,
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$ XNORM, INFO )
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IF( INFO.LT.0 )
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$ NINFO( 1 ) = NINFO( 1 ) + 1
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IF( INFO.GT.0 )
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$ NINFO( 2 ) = NINFO( 2 ) + 1
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IF( ITRANS.EQ.1 ) THEN
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TMP = A( 1, 2 )
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A( 1, 2 ) = A( 2, 1 )
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A( 2, 1 ) = TMP
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END IF
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RES = ABS( ( CA*A( 1, 1 )-WR*D1 )*
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$ X( 1, 1 )+( CA*A( 1, 2 ) )*
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$ X( 2, 1 )+( WI*D1 )*X( 1, 2 )-
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$ SCALE*B( 1, 1 ) )
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RES = RES + ABS( ( CA*A( 1,
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$ 1 )-WR*D1 )*X( 1, 2 )+
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$ ( CA*A( 1, 2 ) )*X( 2, 2 )-
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$ ( WI*D1 )*X( 1, 1 )-SCALE*
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$ B( 1, 2 ) )
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RES = RES + ABS( ( CA*A( 2, 1 ) )*
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$ X( 1, 1 )+( CA*A( 2, 2 )-WR*D2 )*
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$ X( 2, 1 )+( WI*D2 )*X( 2, 2 )-
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$ SCALE*B( 2, 1 ) )
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RES = RES + ABS( ( CA*A( 2, 1 ) )*
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$ X( 1, 2 )+( CA*A( 2, 2 )-WR*D2 )*
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$ X( 2, 2 )-( WI*D2 )*X( 2, 1 )-
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$ SCALE*B( 2, 2 ) )
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IF( INFO.EQ.0 ) THEN
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DEN = MAX( EPS*( MAX( ABS( CA*A( 1,
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$ 1 )-WR*D1 )+ABS( CA*A( 1,
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$ 2 ) )+ABS( WI*D1 ),
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$ ABS( CA*A( 2,
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$ 1 ) )+ABS( CA*A( 2,
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$ 2 )-WR*D2 )+ABS( WI*D2 ) )*
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$ MAX( ABS( X( 1,
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$ 1 ) )+ABS( X( 2, 1 ) ),
|
|
$ ABS( X( 1, 2 ) )+ABS( X( 2,
|
|
$ 2 ) ) ) ), SMLNUM )
|
|
ELSE
|
|
DEN = MAX( EPS*( MAX( SMIN / EPS,
|
|
$ MAX( ABS( CA*A( 1,
|
|
$ 1 )-WR*D1 )+ABS( CA*A( 1,
|
|
$ 2 ) )+ABS( WI*D1 ),
|
|
$ ABS( CA*A( 2,
|
|
$ 1 ) )+ABS( CA*A( 2,
|
|
$ 2 )-WR*D2 )+ABS( WI*D2 ) ) )*
|
|
$ MAX( ABS( X( 1,
|
|
$ 1 ) )+ABS( X( 2, 1 ) ),
|
|
$ ABS( X( 1, 2 ) )+ABS( X( 2,
|
|
$ 2 ) ) ) ), SMLNUM )
|
|
END IF
|
|
RES = RES / DEN
|
|
IF( ABS( X( 1, 1 ) ).LT.UNFL .AND.
|
|
$ ABS( X( 2, 1 ) ).LT.UNFL .AND.
|
|
$ ABS( X( 1, 2 ) ).LT.UNFL .AND.
|
|
$ ABS( X( 2, 2 ) ).LT.UNFL .AND.
|
|
$ ABS( B( 1, 1 ) )+
|
|
$ ABS( B( 2, 1 ) ).LE.SMLNUM*
|
|
$ ( ABS( CA*A( 1, 1 )-WR*D1 )+
|
|
$ ABS( CA*A( 1, 2 ) )+ABS( CA*A( 2,
|
|
$ 1 ) )+ABS( CA*A( 2,
|
|
$ 2 )-WR*D2 )+ABS( WI*D2 )+ABS( WI*
|
|
$ D1 ) ) )RES = ZERO
|
|
IF( SCALE.GT.ONE )
|
|
$ RES = RES + ONE / EPS
|
|
RES = RES + ABS( XNORM-
|
|
$ MAX( ABS( X( 1, 1 ) )+ABS( X( 1,
|
|
$ 2 ) ), ABS( X( 2,
|
|
$ 1 ) )+ABS( X( 2, 2 ) ) ) ) /
|
|
$ MAX( SMLNUM, XNORM ) / EPS
|
|
IF( INFO.NE.0 .AND. INFO.NE.1 )
|
|
$ RES = RES + ONE / EPS
|
|
KNT = KNT + 1
|
|
IF( RES.GT.RMAX ) THEN
|
|
LMAX = KNT
|
|
RMAX = RES
|
|
END IF
|
|
110 CONTINUE
|
|
120 CONTINUE
|
|
130 CONTINUE
|
|
140 CONTINUE
|
|
150 CONTINUE
|
|
160 CONTINUE
|
|
170 CONTINUE
|
|
180 CONTINUE
|
|
190 CONTINUE
|
|
*
|
|
RETURN
|
|
*
|
|
* End of SGET31
|
|
*
|
|
END
|