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261 lines
6.4 KiB
261 lines
6.4 KiB
2 years ago
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*> \brief \b SROTMG
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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 SROTMG(SD1,SD2,SX1,SY1,SPARAM)
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*
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* .. Scalar Arguments ..
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* REAL SD1,SD2,SX1,SY1
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* ..
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* .. Array Arguments ..
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* REAL SPARAM(5)
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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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*> CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS
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*> THE SECOND COMPONENT OF THE 2-VECTOR (SQRT(SD1)*SX1,SQRT(SD2)*> SY2)**T.
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*> WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS..
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*>
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*> SFLAG=-1.E0 SFLAG=0.E0 SFLAG=1.E0 SFLAG=-2.E0
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*>
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*> (SH11 SH12) (1.E0 SH12) (SH11 1.E0) (1.E0 0.E0)
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*> H=( ) ( ) ( ) ( )
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*> (SH21 SH22), (SH21 1.E0), (-1.E0 SH22), (0.E0 1.E0).
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*> LOCATIONS 2-4 OF SPARAM CONTAIN SH11,SH21,SH12, AND SH22
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*> RESPECTIVELY. (VALUES OF 1.E0, -1.E0, OR 0.E0 IMPLIED BY THE
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*> VALUE OF SPARAM(1) ARE NOT STORED IN SPARAM.)
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*>
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*> THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE
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*> INEXACT. THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE
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*> OF SD1 AND SD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM.
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*>
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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[in,out] SD1
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*> \verbatim
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*> SD1 is REAL
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*> \endverbatim
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*>
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*> \param[in,out] SD2
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*> \verbatim
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*> SD2 is REAL
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*> \endverbatim
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*>
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*> \param[in,out] SX1
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*> \verbatim
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*> SX1 is REAL
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*> \endverbatim
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*>
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*> \param[in] SY1
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*> \verbatim
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*> SY1 is REAL
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*> \endverbatim
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*>
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*> \param[out] SPARAM
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*> \verbatim
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*> SPARAM is REAL array, dimension (5)
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*> SPARAM(1)=SFLAG
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*> SPARAM(2)=SH11
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*> SPARAM(3)=SH21
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*> SPARAM(4)=SH12
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*> SPARAM(5)=SH22
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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_blas_level1
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*
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* =====================================================================
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SUBROUTINE SROTMG(SD1,SD2,SX1,SY1,SPARAM)
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*
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* -- Reference BLAS level1 routine --
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* -- Reference BLAS 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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REAL SD1,SD2,SX1,SY1
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* ..
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* .. Array Arguments ..
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REAL SPARAM(5)
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* ..
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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REAL GAM,GAMSQ,ONE,RGAMSQ,SFLAG,SH11,SH12,SH21,SH22,SP1,SP2,SQ1,
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$ SQ2,STEMP,SU,TWO,ZERO
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS
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* ..
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* .. Data statements ..
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*
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DATA ZERO,ONE,TWO/0.E0,1.E0,2.E0/
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DATA GAM,GAMSQ,RGAMSQ/4096.E0,1.67772E7,5.96046E-8/
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* ..
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IF (SD1.LT.ZERO) THEN
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* GO ZERO-H-D-AND-SX1..
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SFLAG = -ONE
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SH11 = ZERO
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SH12 = ZERO
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SH21 = ZERO
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SH22 = ZERO
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*
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SD1 = ZERO
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SD2 = ZERO
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SX1 = ZERO
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ELSE
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* CASE-SD1-NONNEGATIVE
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SP2 = SD2*SY1
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IF (SP2.EQ.ZERO) THEN
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SFLAG = -TWO
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SPARAM(1) = SFLAG
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RETURN
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END IF
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* REGULAR-CASE..
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SP1 = SD1*SX1
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SQ2 = SP2*SY1
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SQ1 = SP1*SX1
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*
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IF (ABS(SQ1).GT.ABS(SQ2)) THEN
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SH21 = -SY1/SX1
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SH12 = SP2/SP1
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*
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SU = ONE - SH12*SH21
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*
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IF (SU.GT.ZERO) THEN
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SFLAG = ZERO
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SD1 = SD1/SU
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SD2 = SD2/SU
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SX1 = SX1*SU
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ELSE
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* This code path if here for safety. We do not expect this
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* condition to ever hold except in edge cases with rounding
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* errors. See DOI: 10.1145/355841.355847
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SFLAG = -ONE
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SH11 = ZERO
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SH12 = ZERO
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SH21 = ZERO
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SH22 = ZERO
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*
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SD1 = ZERO
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SD2 = ZERO
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SX1 = ZERO
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END IF
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ELSE
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IF (SQ2.LT.ZERO) THEN
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* GO ZERO-H-D-AND-SX1..
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SFLAG = -ONE
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SH11 = ZERO
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SH12 = ZERO
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SH21 = ZERO
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SH22 = ZERO
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*
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SD1 = ZERO
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SD2 = ZERO
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SX1 = ZERO
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ELSE
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SFLAG = ONE
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SH11 = SP1/SP2
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SH22 = SX1/SY1
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SU = ONE + SH11*SH22
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STEMP = SD2/SU
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SD2 = SD1/SU
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SD1 = STEMP
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SX1 = SY1*SU
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END IF
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END IF
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* PROCEDURE..SCALE-CHECK
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IF (SD1.NE.ZERO) THEN
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DO WHILE ((SD1.LE.RGAMSQ) .OR. (SD1.GE.GAMSQ))
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IF (SFLAG.EQ.ZERO) THEN
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SH11 = ONE
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SH22 = ONE
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SFLAG = -ONE
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ELSE
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SH21 = -ONE
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SH12 = ONE
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SFLAG = -ONE
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END IF
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IF (SD1.LE.RGAMSQ) THEN
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SD1 = SD1*GAM**2
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SX1 = SX1/GAM
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SH11 = SH11/GAM
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SH12 = SH12/GAM
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ELSE
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SD1 = SD1/GAM**2
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SX1 = SX1*GAM
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SH11 = SH11*GAM
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SH12 = SH12*GAM
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END IF
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ENDDO
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END IF
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IF (SD2.NE.ZERO) THEN
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DO WHILE ( (ABS(SD2).LE.RGAMSQ) .OR. (ABS(SD2).GE.GAMSQ) )
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IF (SFLAG.EQ.ZERO) THEN
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SH11 = ONE
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SH22 = ONE
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SFLAG = -ONE
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ELSE
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SH21 = -ONE
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SH12 = ONE
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SFLAG = -ONE
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END IF
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IF (ABS(SD2).LE.RGAMSQ) THEN
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SD2 = SD2*GAM**2
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SH21 = SH21/GAM
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SH22 = SH22/GAM
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ELSE
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SD2 = SD2/GAM**2
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SH21 = SH21*GAM
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SH22 = SH22*GAM
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END IF
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END DO
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END IF
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END IF
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IF (SFLAG.LT.ZERO) THEN
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SPARAM(2) = SH11
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SPARAM(3) = SH21
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SPARAM(4) = SH12
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SPARAM(5) = SH22
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ELSE IF (SFLAG.EQ.ZERO) THEN
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SPARAM(3) = SH21
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SPARAM(4) = SH12
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ELSE
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SPARAM(2) = SH11
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SPARAM(5) = SH22
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END IF
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SPARAM(1) = SFLAG
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RETURN
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*
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* End of SROTMG
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*
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END
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