252 lines
6.2 KiB
Fortran
252 lines
6.2 KiB
Fortran
*> \brief \b DROTMG
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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 DROTMG(DD1,DD2,DX1,DY1,DPARAM)
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*
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* .. Scalar Arguments ..
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* DOUBLE PRECISION DD1,DD2,DX1,DY1
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION DPARAM(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 (DSQRT(DD1)*DX1,DSQRT(DD2)*> DY2)**T.
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*> WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS..
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*>
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*> DFLAG=-1.D0 DFLAG=0.D0 DFLAG=1.D0 DFLAG=-2.D0
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*>
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*> (DH11 DH12) (1.D0 DH12) (DH11 1.D0) (1.D0 0.D0)
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*> H=( ) ( ) ( ) ( )
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*> (DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0).
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*> LOCATIONS 2-4 OF DPARAM CONTAIN DH11, DH21, DH12, AND DH22
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*> RESPECTIVELY. (VALUES OF 1.D0, -1.D0, OR 0.D0 IMPLIED BY THE
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*> VALUE OF DPARAM(1) ARE NOT STORED IN DPARAM.)
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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 DD1 AND DD2. 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] DD1
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*> \verbatim
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*> DD1 is DOUBLE PRECISION
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*> \endverbatim
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*>
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*> \param[in,out] DD2
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*> \verbatim
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*> DD2 is DOUBLE PRECISION
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*> \endverbatim
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*>
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*> \param[in,out] DX1
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*> \verbatim
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*> DX1 is DOUBLE PRECISION
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*> \endverbatim
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*>
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*> \param[in] DY1
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*> \verbatim
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*> DY1 is DOUBLE PRECISION
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*> \endverbatim
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*>
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*> \param[out] DPARAM
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*> \verbatim
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*> DPARAM is DOUBLE PRECISION array, dimension (5)
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*> DPARAM(1)=DFLAG
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*> DPARAM(2)=DH11
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*> DPARAM(3)=DH21
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*> DPARAM(4)=DH12
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*> DPARAM(5)=DH22
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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 2017
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*
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*> \ingroup double_blas_level1
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*
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* =====================================================================
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SUBROUTINE DROTMG(DD1,DD2,DX1,DY1,DPARAM)
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*
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* -- Reference BLAS level1 routine (version 3.8.0) --
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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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* November 2017
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*
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* .. Scalar Arguments ..
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DOUBLE PRECISION DD1,DD2,DX1,DY1
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION DPARAM(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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DOUBLE PRECISION DFLAG,DH11,DH12,DH21,DH22,DP1,DP2,DQ1,DQ2,DTEMP,
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$ DU,GAM,GAMSQ,ONE,RGAMSQ,TWO,ZERO
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DABS
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* ..
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* .. Data statements ..
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*
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DATA ZERO,ONE,TWO/0.D0,1.D0,2.D0/
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DATA GAM,GAMSQ,RGAMSQ/4096.D0,16777216.D0,5.9604645D-8/
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* ..
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IF (DD1.LT.ZERO) THEN
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* GO ZERO-H-D-AND-DX1..
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DFLAG = -ONE
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DH11 = ZERO
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DH12 = ZERO
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DH21 = ZERO
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DH22 = ZERO
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*
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DD1 = ZERO
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DD2 = ZERO
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DX1 = ZERO
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ELSE
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* CASE-DD1-NONNEGATIVE
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DP2 = DD2*DY1
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IF (DP2.EQ.ZERO) THEN
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DFLAG = -TWO
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DPARAM(1) = DFLAG
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RETURN
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END IF
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* REGULAR-CASE..
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DP1 = DD1*DX1
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DQ2 = DP2*DY1
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DQ1 = DP1*DX1
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*
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IF (DABS(DQ1).GT.DABS(DQ2)) THEN
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DH21 = -DY1/DX1
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DH12 = DP2/DP1
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*
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DU = ONE - DH12*DH21
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*
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IF (DU.GT.ZERO) THEN
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DFLAG = ZERO
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DD1 = DD1/DU
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DD2 = DD2/DU
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DX1 = DX1*DU
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END IF
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ELSE
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IF (DQ2.LT.ZERO) THEN
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* GO ZERO-H-D-AND-DX1..
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DFLAG = -ONE
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DH11 = ZERO
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DH12 = ZERO
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DH21 = ZERO
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DH22 = ZERO
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*
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DD1 = ZERO
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DD2 = ZERO
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DX1 = ZERO
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ELSE
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DFLAG = ONE
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DH11 = DP1/DP2
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DH22 = DX1/DY1
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DU = ONE + DH11*DH22
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DTEMP = DD2/DU
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DD2 = DD1/DU
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DD1 = DTEMP
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DX1 = DY1*DU
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END IF
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END IF
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* PROCEDURE..SCALE-CHECK
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IF (DD1.NE.ZERO) THEN
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DO WHILE ((DD1.LE.RGAMSQ) .OR. (DD1.GE.GAMSQ))
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IF (DFLAG.EQ.ZERO) THEN
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DH11 = ONE
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DH22 = ONE
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DFLAG = -ONE
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ELSE
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DH21 = -ONE
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DH12 = ONE
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DFLAG = -ONE
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END IF
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IF (DD1.LE.RGAMSQ) THEN
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DD1 = DD1*GAM**2
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DX1 = DX1/GAM
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DH11 = DH11/GAM
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DH12 = DH12/GAM
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ELSE
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DD1 = DD1/GAM**2
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DX1 = DX1*GAM
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DH11 = DH11*GAM
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DH12 = DH12*GAM
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END IF
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ENDDO
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END IF
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IF (DD2.NE.ZERO) THEN
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DO WHILE ( (DABS(DD2).LE.RGAMSQ) .OR. (DABS(DD2).GE.GAMSQ) )
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IF (DFLAG.EQ.ZERO) THEN
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DH11 = ONE
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DH22 = ONE
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DFLAG = -ONE
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ELSE
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DH21 = -ONE
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DH12 = ONE
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DFLAG = -ONE
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END IF
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IF (DABS(DD2).LE.RGAMSQ) THEN
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DD2 = DD2*GAM**2
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DH21 = DH21/GAM
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DH22 = DH22/GAM
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ELSE
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DD2 = DD2/GAM**2
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DH21 = DH21*GAM
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DH22 = DH22*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 (DFLAG.LT.ZERO) THEN
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DPARAM(2) = DH11
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DPARAM(3) = DH21
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DPARAM(4) = DH12
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DPARAM(5) = DH22
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ELSE IF (DFLAG.EQ.ZERO) THEN
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DPARAM(3) = DH21
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DPARAM(4) = DH12
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ELSE
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DPARAM(2) = DH11
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DPARAM(5) = DH22
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END IF
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DPARAM(1) = DFLAG
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RETURN
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END
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